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A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross
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A casino patron will continue to make $5 bets on red in

Chapter 4, Problem 18STE

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QUESTION:

Problem 18STE

A casino patron will continue to make $5 bets on red in roulette until she has won 4 of these bets.

(a) What is the probability that she places a total of 9 bets?

(b) What are her expected winnings when she stops? Remark: On each bet, she will either win $5 with probability  or lose $5 with probability .

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QUESTION:

Problem 18STE

A casino patron will continue to make $5 bets on red in roulette until she has won 4 of these bets.

(a) What is the probability that she places a total of 9 bets?

(b) What are her expected winnings when she stops? Remark: On each bet, she will either win $5 with probability  or lose $5 with probability .

ANSWER:

Answer

Step 1 of 2

(a)

We are asked to find the probability that she places a total of  bets.

We have given a casino patron will continue to make $5 bets on red in roulette until she has won 4 of these bets.

Let  denote the number of bets.

On each bet, she will either win $5 with probability  or lose $5 with probability

Since  follows a binomial random variable, we know a binomial distribution

We have given

We need to calculate  since 3 rounds are required and last round (9th round) will also include in the calculation with probability

Hence we can write,

Hence the probability that she places a total of  bets is

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