1. Suppose that two teams play a series of games that ends when one of them has won 2 games. Assume that each game played is, independently, won by team A with probability or by B with probability. Find the expected number of games that are played in the series. 2. Two coins are to be flipped. The first coin will land on heads with probability 0.5, the second with probability 0.6. Assume that the results of the flips are independent, and let X be the total number

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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1. Suppose that two teams play a series of games that ends when one of them has won 2 games.
Assume that each game played is, independently, won by team A with probability or by B with
probability. Find the expected number of games that are played in the series.
2. Two coins are to be flipped. The first coin will land on heads with probability 0.5, the second with
probability 0.6. Assume that the results of the flips are independent, and let X be the total number
of heads that results. Determine E(X) and Var(X).
3. Four buses carry, respectively, 40, 33, 27, and 50 students. One of the students is randomly selected.
Let X be the number of students who were on the bus carrying the selected student, and set
Y = -3 + ln X. Compute E(Y) and round your answer to four decimal places.
Transcribed Image Text:1. Suppose that two teams play a series of games that ends when one of them has won 2 games. Assume that each game played is, independently, won by team A with probability or by B with probability. Find the expected number of games that are played in the series. 2. Two coins are to be flipped. The first coin will land on heads with probability 0.5, the second with probability 0.6. Assume that the results of the flips are independent, and let X be the total number of heads that results. Determine E(X) and Var(X). 3. Four buses carry, respectively, 40, 33, 27, and 50 students. One of the students is randomly selected. Let X be the number of students who were on the bus carrying the selected student, and set Y = -3 + ln X. Compute E(Y) and round your answer to four decimal places.
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