+ P(AA n) Oct 1, 2019 · Unconditional probability is the likelihood that an event will end with a specific result irrespective of other conditions that may be present. P ( F) = the probability of majoring in finance. To find P ( B | A), the probability that B occurs given that A has occurred, Bayes’ Rule states the following: This says that conditional probability is the probability that both A and B occur divided by the unconditional probability that A occurs. 0198. If p (T) = 0. 7 = 0. In conditional probability, we find the occurrence of an event given that another event has already occurred. P (B | A) = P (A ∩ B) / P (A) Conditional probability = 0. Joint probability : p (A and B). You can then find the unconditional probabilities of the following events directly from the table: P ( B) = the probability of pursuing a bachelor's degree. Conditional probabilities, conditional expectations, and conditional probability distributions are treated on three levels: discrete probabilities, probability density functions, and measure theory. e. 1*2}$ = 8. In other words, the conditional Jun 4, 2020 · About the connection between the conditional and unconditional probabilities of events see Bayes formula and Complete probability formula. In this case P(A|B) = P(A ∩ B)/P(B) P ( A | B) = P ( A ∩ B) / P ( B). Given two jointly distributed random variables and , the conditional probability distribution of given is the May 16, 2016 · Where the probability of default in the second year (only second year without any consideration of what happened in the prior year) = Unconditional Probability. ”. Therefore, if a buyer chosen at random is found to have purchased brown bread, then there is a 60% chance that he has also purchased peanut butter. P(1st red and 2nd white) = P(1st red) ⋅ P(2nd white) = 5 9 ⋅ 4 9 = 20 81. Unconditional probability. Given two random variables that are defined on the same probability space, [1] the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. This means that the likelihood of the Dow going up in any given month, regardless of interest rate movements, is 0. Marginal and Joint Probabilities Conditional probability close probability The extent to which something is likely to be the case. Jul 3, 2024 · Let’s consider two events A and B, then the formula for conditional probability of A when B has already occurred is given by: P (A|B) = P (A ∩ B) / P (B) Where, P (A ∩ B) represents the probability of both events A and B occurring simultaneously. Khan Academy is a free online learning platform that covers various topics in math, science, and more. We can use the General Multiplication Rule when two events are dependent. The empirical probability is P(E) = 2. The conditional probability of B, given A is written as P(B|A) P ( B | A), and is read as “the probability of B given A happened first. Conditional Probability = 0. 4 Probability Formulae for the AQA A Level Maths: Statistics Nov 23, 2020 · The probability for statement one is roughly 50% or (1/2). 65), then the unconditional probability of the train not arriving on time p (T c) = 1 – p (T) = 1 – 0. Mar 27, 2023 · Events A A and B B are independent (i. This question can be solved using the total probability rule. Jul 9, 2019 · 1. Particularly in econometrics, the conditional variance is also known as the scedastic function or skedastic function. Thus, the probability that any child is selected is 1/5,290 = 0. The correct answer is B. tain medical condition. Working of Empirical Probability Calculator: Jul 24, 2016 · P(B) is the unconditional probability of a positive test; here it is 198/10,000 = 0. The Conditional Probability Formula. If we select a child at random (by simple random sampling), then each child has the same probability (equal chance) of being selected, and the probability is 1/N, where N=the population size. Our interest lies in the probability of an event ‘A’ given that another event ‘B ‘ has already occurred. In probability theory and statistics, the conditional probability distribution is a probability distribution that describes the probability of an outcome given the occurrence of a particular event. This is a simple algebraic restatement of a 1 Probability, Conditional Probability and Bayes Formula The intuition of chance and probability develops at very early ages. 16) Law of Total Expectation: Conditional Probability. Since there are 5 school days in a week, the probability that it is Friday is 0. Trustpilot rating score: 4. Feb 3, 2024 · A borrower's credit rating reflects their probability of default. But the probability that it lands with ‘5’ showing up, given that it lands with an odd number showing up, is 1/3; this is a conditional probability. Conditional Scenario: What if it rains the team's chances may change (for the better or possibly for the worse)? The probability of winning is affected by the weather - conditional. My doubt is, if event B has already occurred , it would mean that our reduced sample space is the entire set of B. 1 Conditional Probability for Drawing Cards without Replacement. In this case write P(A|B) P ( A | B), taking out θ θ. 95) whereas the probability that he plays given that it is a rainy day is less which is 10% (0. According to clinical trials, the test has t. In this chapter, the differences between risk-free and default risky interest rates are discussed together with credit spreads and default probability approximations with respect to credit spreads. star content check off when done. Line graphs were used to depict time trends in age-specific mortality rates over the years in four major NCDs (cardiovascular diseases, cancer, diabetes, and chronic respiratory With multiple conditions, I find it easiest to think about it this way: temporarily remove the condition (s) that you want to remain as conditions in your result. If the experiment can be repeated potentially infinitely many times, then the probability of an event can be defined through relative frequencies. $\endgroup$ – . Solution: Let event A is a heart on the first draw, and event B is a heart on the second draw. 2. 65. His work was published in 1763 as An Essay Towards Solving a Problem in the Doctrine of Chances. To get a visual understanding of this, one can refer to the Venn diagram for conditional probability P(A For instance, a team might have a probability of 0. Furthermore, the unconditional probability that the robot signals a defective item can be derived using the law of total probability: Therefore, Bayes' rule gives. hide. The conditional probability, as its name suggests, is the probability of happening an event that is based upon a condition. (Hint: look for the word “given” in the After an ace is drawn on the first draw, there are 3 aces out of 51 total cards left. 1). You need to find the unconditional probability of a stock rise under all circumstances. In probability theory and statistics, a conditional variance is the variance of a random variable given the value (s) of one or more other variables. pij is the probability for the markov chain to be in state i at time t knowing it is in state j at time t-1. Outcome 2: What is the probability of the event “both children are girls” (B) conditional on the event “at least one of the children is a girl” (L)? The probability for statement two is roughly 33% or (1/3). Feb 15, 2021 · The grand total is the number of outcomes for the denominator. We Bayes' theorem is named after the Reverend Thomas Bayes ( / beɪz / ), also a statistician and philosopher. What we want to know is P (A | B), i. Consider any two events A and B. Therefore, Jul 24, 2023 · Conditional probability is calculated using the formula given below. P(A, B, C) = P(A)P(B)P(C) Example 13. Continuing with the previous example, if the total number of borrowers is 100, and 10 of them have defaulted after one year, the unconditional default probability after one year would be 10 100 = 0. 1, or 10%. What is the probability that a student is absent given that today is Friday? Solution: Mar 19, 2024 · Moreover, unconditional probability differs from joint probability, where the focus is on assessing the likelihood of two or more outcomes occurring simultaneously (\(P(A ∩ B)\)). What is the probability of surviving in the first year followed by defaulting in the second? My solution was to calculate the marginal probability of default = $0. P (A∩B) signifies the joint probability of both events occurring. To calculate a conditional probability we need the joint probability of two events. Find the following probabilities: The probability that the second card is a heart given that the first card is a spade. P r o b a b i l i t y = n u m b e r o f f a v o r a b l e o u Conditional Probability. The conditional probability of an event $ A $ with respect to a $ \sigma $- algebra $ \mathfrak B $ is a random variable $ {\mathsf P} ( A \mid \mathfrak B ) $, measurable relative to $ \mathfrak B $, for which Dec 19, 2023 · Posterior Probability: The revised probability of an event occurring after taking into consideration new information. The joint distribution can just as well be considered for any given number of random variables. Probabilities are either unconditional or conditional. Conditional Probability. , probability market will be up for the day Conditional: P(A|B), the probability of A given that B has occurred, e. if. And the conditional probability, that he eats a bagel for breakfast given that he eats a pizza for lunch, so probability of event A happening, that he eats a bagel for breakfast, given that he's had a pizza for lunch is equal to 0. It may be computed by means of the following formula: P(A ∣ B) = P(A ∩ B) P(B) Apr 15, 2024 · With this example, you could clearly see how the probability of an event changes depending on the information we have. Revision notes on 3. P (B) represents the probability of event B occurring. The lowest-rated issues, on the other hand, often default early Mar 11, 2023 · P(A ∩ B) This is read as the probability of the intersection of A and B. T = majoring in marketing. 33 and the experimental and theoretical probability calculator can be a simple solution to know the experimental and theoretical probability ratio. The player who plays first has the advantage of going first; that player can win the game in the first round, but cannot lose the game in the first round. P(A ∩ B) = P(A) ⋅ P(B) P ( A ∩ B) = P ( A) ⋅ P ( B) If A A and B B are not independent then they are dependent. Definition Let and be two random variables. An unconditional probability is the chance of occurrence of a single outcome among the several possible outcomes. Proof: Let S be the sample space. Unconditional probability is calculated by dividing the instances of a definite outcome by the total number of events. A joint probability is the probability of event A and event B happening, P(A and B). The unconditional probability of event A is denoted P (A) and is sometimes referred to as marginal probability. 4) (5. Solution. 0002. This means that the conditional probability of drawing an ace after one ace has already been drawn is 3 51 = 117 3 51 = 1 17. It is the likelihood of the intersection of two or more events. But the probability that it lands with ‘5’ showing up, given that it lands with an odd number showing up, is 1/3; this is a conditional probability. May 6, 2020 · Marginal Probability: Probability of event X=A given variable Y. Improve this question. Dec 1, 2003 · It is proved that every probability assignment has uncountably many ‘trouble spots’, andConditional probability should be taken as the primitive notion, and unconditional probabilityshould be analyzed in terms of it. The conditional probability formula is P (A|B) = P (AnB) / P (B). In the sample, 50% of trains were destined for New York, 30% Vegas and 20% Washington DC. 714. Aug 5, 2019 · The correct answer is A. Following the Law of Total Probability, we state Bayes' Rule, which is really just an application of the Multiplication Law. . Condition on the result of the first round and set up an equation to solve for \ (p\). The probabilities of a train arriving late in New York, Vegas, and Washington DC are 40%, 35%, and 25% Nov 25, 2016 · The transition probability matrix is pij, i, j from 1 to 3. 1. 35. The probability that it lands with ‘5’ showing up is 1/6; this is an unconditional probability. It is the probability of an event regardless of any conditions. Conditional probability distribution. The joint distribution encodes the marginal Apr 5, 2018 · Is it possible to prove the formula of conditional probability without a venn diagram? conditional-probability; Share. So, the two events are independent and hence the probabilities of occurrence of these two events are unconditional. This formula can only be used if the appropriate probabilities are known: Pr [A and B] and P [B]. But at first glance, they look similar. 33. 1, where the underlying probability experiment was to flip a fair coin three times, and the random variable \(X\) denoted the number of heads obtained and the random variable \(Y\) denoted the winnings when betting on the placement of the first heads Conditional Probabilitypharmaceutical company is marketing a new test for a ce. Let $ X ( \omega ) $, $ \omega \in \Omega $, be a random variable on $ ( \Omega , {\mathcal A} , {\mathsf P}) $, let $ {\mathsf E} X $ be its mathematical expectation and $ {\mathsf E}( X \mid A _ {k} ) $ the conditional mathematical expectations with respect to events $ A Dec 9, 2016 · That doesn't mean Bayes' rule isn't a useful formula, however. A conditional probability is the exact opposite of an unconditional probability. By definition, the conditional probability equals the probability of the intersection of events A and B over the probability of event B occurring: \[P(A|B) = \frac {P (A \cap B)}{P (B)}\] For example, event A refers to an increase in interest rates. Jul 13, 2024 · Here, the theory part is written in black ink irrespective of whether the diagrams are drawn with a pencil or not. The conditional probability formula doesn't give us the probability of A given B. Consequently, to calculate joint probabilities in a contingency table, take each cell count and divide by the grand total. 3. The formula in the definition has two practical but exactly opposite uses: Marginal distribution. p(W, TX) = p(W)p(TX) (5. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team. Show/hide solution. 65 = 0. Conditional probability: It is defined as the possibility of an outcome in an event based on another event. 70. Hence, Marginal Default Probability = Unconditional probability of default in year 2 divided by the probability of survival in year 1. Thus, the probability of both cards being aces is 452 ⋅ 351 = 122652 = 1221 4 52 ⋅ 3 51 = 12 2652 = 1 221. Bayes' Rule is used to calculate what are Jan 1, 2022 · The formula used to calculate hazard rate is -1 * [log(At Risk - Default) - log(At Risk)] and cumulative sum to get cumulative hazard rate, you are taking the difference in cumulative survival calculated that way between two adjacent time periods. , the probability of the occurrence of event A with relation to condition B. 1. restore the condition (s Conditional Probabilitypharmaceutical company is marketing a new test for a ce. It can be calculated using the formula: Unconditional Default Probability = Number of Defaults Total Number of Borrowers. Introduction. , A n where A 1, A 2,. The probability that the first marble is red and the second marble is white is 20 81. Using the total probability rule: P (B) = P (B|A1) × P (A1) + P (B|A2) × P (A2) + P (B|A3) × P (A3) Plug in the known probabilities into the total probability rule, and we get an unconditional probability of 0. It is not conditioned on another event. For example, assume that the probability of a boy playing tennis in the evening is 95% (0. For our example, the joint probability of females buying Macs equals the value in that cell (87) divided by the grand total (223). apply the normal rules. Jun 26, 2024 · The Law of Total Probability then provides a way of using those conditional probabilities of an event, given the partition to compute the unconditional probability of the event. , the probability of disease (A), given that the patient has a positive test (B). Example \(\PageIndex{1}\) For an example of conditional distributions for discrete random variables, we return to the context of Example 5. The probability that the first card is a face card and the The conditional probability is found by dividing the joint probability by the unconditional probability, Pr [B] for the given event. Since the first marble is put back in the bag before the second marble is drawn these are independent events. 3 of winning the World Cup. e. In this formula, the random variable X takes the value xᵢ with probability that is equal to the sum of the probabilities of xᵢ given each value of the random variable Y Conditioning (probability) Beliefs depend on the available information. 3. The probability of event A is 0. Bayes used conditional probability to provide an algorithm (his Proposition 9) that uses evidence to calculate limits on an unknown parameter. , probability that the market will be up for the day, given that the Fed Oct 10, 2019 · Example: Bayes’ Formula. Aug 25, 2021 · The total probability of a stock rise is closest to: 0. Nov 19, 2015 · 1 year hazard rate = 0. The manual states that the lifetime T T of the product, defined as the amount of time (in years) the product works properly until Solved Examples Using Conditional Probability Formula. Question 1: The probability that it is Friday and that a student is absent is 0. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. 65 (Unconditional probability of train arriving on time is 0. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in Jan 13, 2024 · The complete probability formula holds for mathematical expectations. 7 of 5, based on 61 reviews. [1] Conditional variances are important parts of We have already discussed the calculation of the unconditional probability of an event using the total probability rules. The probability of the intersection of A and B is written as P(A ∩ B). P(E) = 7/3. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a The conditional probability P (A|B) is the probability that event A will occur, given that event B has already occurred. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Aug 13, 2019 · The correct answer is B. 5). 0. 5 Solved Problems: Conditional Probability. So shouldn't P (B) = 1 just like how we say P (S Unconditional probability of dying between ages 30 and 70 years during 2001, 2006, and 2013 was calculated by the formula suggested by the World Health Organization. Joint probability incorporates the unconditional probabilities of A and B, providing a comprehensive perspective on the simultaneous occurrence of events. This is completely analogous to the discrete case. Jul 13, 2022 · Level 1 CFA Exam Takeaways: Probability – Practical Problems. This idea is formalized in probability theory by conditioning. Chain rule for conditional probability: Let us write the formula for conditional probability in the following format $$\hspace{100pt} P(A \cap B)=P(A)P(B|A)=P(B)P(A|B) \hspace{100pt} (1. Conditional Probability: Probability of event A given event B. 12%. 7, which is interesting. Know how to tell when events are conditional or independent. e following properties:When applied to an affected person, the test comes up positive in 90% of cases, and negative in 10% (these are c. Two cards are selected randomly from a standard deck of cards (no jokers). In our example, if the percentage of women among freshmen from Texas is known to be the same as the percentage of women among all freshmen, then. In fact, the highest-rated issues almost never default even over a significant period of, say, 10 years. 516% Sep 8, 2023 · 00:00 – Intro00:53 – conditional probability 01:48 – exampleConditional probability is the probability of an event occurring given that another event has alr Mar 12, 2024 · The conditional probability formula for an event that is neither mutually exclusive nor independent is: P (A|B) = P(A∩B)/P (B), where: P (A|B) denotes the conditional chance, i. 30 / 0. Feb 24, 2015 · Concepts of Probability • Unconditional Probability (AKA marginal or prior probability): ─ P(a), the probability of “a” being true ─ Does not depend on anything else to be true (unconditional) ─ Represents the probability prior to further information that may adjust it (prior) • Conditional Probability (AKA posterior probability): As you can see by the formulas, a conditional mean is calculated much like a mean is, except you replace the probability mass function with a conditional probability mass function. 5. The conditional expectation of given is the weighted average of the values that can take on, where each possible value is weighted by its respective conditional probability (conditional on the information that ). A fair die is about to be tossed. In this article, we'll explore what unconditional probability is, how it differs from other types of probability, and provide real-world examples to illustrate its importance in Jan 14, 2023 · Solution. For example: The probability of a row of data is the joint probability across each input The probability of event B, that he eats a pizza for lunch, is 0. Using the calculator is as straightforward as it gets. Compute the joint probabilities using the multiplication rule. Sep 2, 2014 · Conditional vs. 50. t. P ( M) = the probability of pursuing a master's degree. And, a conditional variance is calculated much like a variance is, except you replace the probability mass function with a conditional probability mass function. We know that prevalence of disease (the unconditional probability of disease) is 1% or 0. Problem. In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. These types of probability form the basis of much of predictive modeling with problems such as classification and regression. Posterior probability is normally calculated by updating the prior probability Bayes’ Rule. When applied to a healthy person, the May 23, 2024 · In the realm of probability, conditional probability refers to the likelihood of an event A occurring, given that another event B has already occurred. to Example 7. Example: the probability that a card drawn is red (p (red) = 0. Our Conditional Probability Calculator is a practical tool designed to save time and improve the accuracy of your statistical calculations. 1 However, a formal, precise definition of the probability is elusive. The conditional probability of A given B, denoted P(A ∣ B), is the probability that event A has occurred in a trial of a random experiment for which it is known that event B has definitely occurred. The expectation of a random variable conditional on is denoted by. To solve this, we can use Bayes’ Formula: Draw a tree diagram, if helpful. P (survival) = (1−π)3 = (1−2%)3 = 94. Even if the robot is conditionally very accurate, the unconditional probability that the robot is right when he says that an item is defective is less than 10 per cent! The damage that has been done is that there is a time at which an agent assigns a conditional probability (1 2) in the absence of the corresponding unconditional probabilities required by the ratio formula. The higher the rating, the more financially reliable a borrower is considered to be. AbstractKolmogorov's axiomatization of probability includes the familiarratio formula for conditional probability: $$({\\text{RATIO}}) P(A|B) = \\frac{{P(A \\cap B)}}{{P(B Unconditional probability: It is defined as the occurrence of a particular outcome in an event with several outcomes. In particular, the law of total probability, the law of total expectation (law of iterated expectations), and the law of total variance can be stated as follows: Law of Total Probability: P(A) = ∫∞ − ∞P(A | X = x)fX(x) dx (5. Semantically, I'd say there's always a need to use Bayes' rule, but when A and B are independent the rule can be reduced to a much simpler form. led false negatives ). It is denoted by P(A). 7. 40. As is evident, this is an immediate counterexample to the ratio formula. The probability of event a occurring is equal to the probability of a given b times the probability of b, plus the probability of a given ¬b time the probability of ¬b. Jul 14, 2023 · The probability of event B happening, given that event A already happened, is called the conditional probability. Conditional variance. A c is the event that interest rates will not increase. Marginal probability: the probability of an event occurring (p (A)), it may be thought of as an unconditional probability. Oct 10, 2017 · Unconditional probability of dying between the ages of 30 and 69 years is the probability that a person aged 30 years will die from selected causes of death before reaching the age of 70 years May 22, 2022 · It is the product of the probabilities of the two events. Cite. Two cards are drawn from a well shuffled deck of 52 cards without replacement. , events whose probability of occurring together is the product of their individual probabilities). I know the formula in the case where there are 2 states, but I can't find a general formula, for n states (3 At the heart of probability theory lies the concept of unconditional probability, a term that might sound complex but is integral to understanding the world of finance. A Civil Engineer wishes to investigate the punctuality of electric trains by considering the number of train journeys. Unconditional probability, also called marginal probability, is simply the probability of an event occurring. 4) p ( W, T X) = p ( W) p ( T X) Since it is unusual for two events to be independent, a more general formula Definition: conditional probability. Knowing B has already occurred will change the probability that A will occur (unless A & B are independent events). 6 of winning the Super Bowl or a country a probability of 0. 4. 75. For example, the likelihood that a card is black and seven is equal to P(Black and Seven) = 2/52 = 1/26. 19%. So let me write this down. g. Plug in the figures and calculate the updated probability (in this case, 0 Unconditional probability of dying between ages 30 and 70 years during 2001, 2006, and 2013 was calculated by the formula suggested by the World Health Organization. But the given answer was 8. Now, we can solve for. Example: Find the probability of drawing a heart on each of two consecutive draws from well shuffled-packs of cards if the card is not replaced after the draw. What is conditional probability and how does it relate to independence? Learn how to use formulas and tables to calculate conditional probabilities and check if two events are independent. 61% arrived at by: 1 year cumulative (also called unconditional) PD = 1 - e^(- hazard*time) = 9. Another example: the probability that a card drawn is a 4 (p (four)=1/13). Determine the event (B) and the new information (U). P(E) = 2. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables. In other words, the probability of event A is contingent upon the occurrence of event B. P(A c) = 1 - 0. In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It seamlessly handles the heavy lifting of calculations, enabling you to focus on interpreting the results and making informed decisions. If A, B, and C are independent random variables, then. Try It 6. Conditional Probability Formula: The formula for conditional probability is given as: P(A/B) = \[\frac{N(A\cap B Oct 10, 2019 · The probability that a given stock will earn a 10% annual return without considering the preceding annual returns. The probability of an event does not depend on the outcome of previous events. We would like to show you a description here but the site won’t allow us. If the event A is dependent on event A 1, A 2,. This implies that higher-rated issues have a lower probability of default. It In this Refresher Reading, learn basic probability issues such as mutual exclusivity, probability and odds, conditional and unconditional probability, multiplication and addition rules, dependent and independent events, covariance and Bayes formula. Jun 28, 2003 · Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. In die and coin problems, unless stated otherwise, it is assumed coins and dice are fair and repeated trials are independent. . So the formula of P (A|B) = P (intersection of A and B) over P (B). Line graphs were used to depict time trends in age-specific mortality rates over the years in four major NCDs (cardiovascular diseases, cancer, diabetes, and chronic respiratory Jan 1, 2011 · 1. Between each draw the card chosen is replaced back in the deck. 1\lambda e^{0. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in The empirical probability formula is: P(E) = f/n. Calculate the unconditional probability of U using the total probability rule. When applied to a healthy person, the v. For example, if a die lands on the number five 15 times out of 60 , the Jul 24, 2016 · Unconditional Probability. For example, in a class of 50 girls and 20 boys, the probability of choosing a girl is 50/70 = 0. 1 5. 55. Jan 11, 2022 · Example 5. , A n are mutually exclusive and exhaustive events then according to the total probability rule: P(A) = P(AA 1) + P(AA 2) + P(AA 3) + . 01; this is represented by P(A). 5)$$ This format is particularly useful in situations when we know the conditional probability, but we are interested in the probability of the intersection. 03. occurs when it is given that something has happened. Unconditional Two types of probability: Unconditional: P(A), the probability of an event regardless of the outcomes of other events, e. You purchase a certain product. I'm a looking for the non conditional probability: P (state in t=j). mu hs lg pu ib bn yy vw ti zj