Bob is a recent law school graduate who intends to take the state bar exam. According to the National Conference on Bar Examiners, about 56% of all people who take the state bar exam pass. Let n = 1, 2, 3, ... represent the number of times a person takes the bar exam until the first pass. (a) Write out a formula for the probability distribution of the random variable n. (Use p and n in your answer.) P(n) = (b) What is the probability that Bob first passes the bar exam on the second try (n = 2)? (Use 3 decimal places.) (c) What is the probability that Bob needs three attempts to pass the bar exam? (Use 3 decimal places.) (d) What is the probability that Bob needs more than three attempts to pass the bar exam? (Use 3 decimal places.) (e) What is the expected number of attempts at the state bar exam Bob must make for his (first) pass? Hint: Use ? for the geometric distribution and round.
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
Bob is a recent law school graduate who intends to take the state bar exam. According to the National Conference on Bar Examiners, about 56% of all people who take the state bar exam pass. Let n = 1, 2, 3, ... represent the number of times a person takes the bar exam until the first pass.
P(n) =
(b) What is the probability that Bob first passes the bar exam on the second try (n = 2)? (Use 3 decimal places.)
(c) What is the probability that Bob needs three attempts to pass the bar exam? (Use 3 decimal places.)
(d) What is the probability that Bob needs more than three attempts to pass the bar exam? (Use 3 decimal places.)
(e) What is the expected number of attempts at the state bar exam Bob must make for his (first) pass? Hint: Use ? for the geometric distribution and round.
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