Susan is taking Western Civilization this semester on a pass/fail basis. The department teaching the course has a history of passing 88% of the students in Western Civilization each term. Let n = 1, 2, 3, represent the number of times a student takes Western Civilization until the first passing grade is received. (Assume the trials are independent.) (a) Write out a formula for the probability distribution of the random variable n. P(n) = (b) What is the probability that Susan passes on the first try (n = 1)? (Round your answer to two decimal places.) (c) What is the probability that Susan first passes on the second try (n = 2)? (Round your answer to three decimal places.)
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.
Susan is taking Western Civilization this semester on a pass/fail basis. The department teaching the course has a history of passing 88% of the students in Western Civilization each term. Let
represent the number of times a student takes Western Civilization until the first passing grade is received. (Assume the trials are independent.)
P(n) =
(b) What is the probability that Susan passes on the first try (n = 1)? (Round your answer to two decimal places.)
(c) What is the probability that Susan first passes on the second try (n = 2)? (Round your answer to three decimal places.)
(d) What is the probability that Susan needs three or more tries to pass Western Civilization? (Round your answer to three decimal places.)
(e) What is the expected number of attempts at Western Civilization Susan must make to have her (first) pass? Hint: Use ? for the geometric distribution and round. (Round your answer to two decimal places.)
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