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Let X be the winnings of a gambler. Let p(i) = P(X = i)

A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross ISBN: 9780321794772 63

Solution for problem 10P Chapter 4

A First Course in Probability | 9th Edition

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A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross

A First Course in Probability | 9th Edition

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Problem 10P

Problem 10P

Let X be the winnings of a gambler. Let p(i) = P(X = i) and suppose that

P(0) = 1/3; P(1) = P(-1) = 13/55;

p(2)=p(-2) = 1/11; p(3) = p(-3) = 1/165

Compute the conditional probability that the gambler

Step-by-Step Solution:

Answer

Step 1 of 1

(a)

Let  be the winnings of a gambler.

Let  and suppose that

We are asked to compute the conditional probability that the gambler wins  given that he wins a positive amount.

Let  be the event that we win something.

We need to find

Using Bayes’ rule we can write that

……(1)

So that we have  when

Hence the conditional probability that the gambler wins


Step 2 of 1

Chapter 4, Problem 10P is Solved
Textbook: A First Course in Probability
Edition: 9
Author: Sheldon Ross
ISBN: 9780321794772

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Let X be the winnings of a gambler. Let p(i) = P(X = i)