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

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