Question

Let $X$ be the winnings of a gambler. Let $p(i)=$ $P(X=i)$ and suppose that $$\begin{array}{l} p(0)=1 / 3 ; p(1)=p(-1)=13 / 55 \\ p(2)=p(-2)=1 / 11 ; p(3)=p(-3)=1 / 165 \end{array}$$ Compute the conditional probability that the gambler wins $i, i=1,2,3,$ given that he wins a positive amount.

          Let $X$ be the winnings of a gambler. Let $p(i)=$ $P(X=i)$ and suppose that
$$\begin{array}{l}
p(0)=1 / 3 ; p(1)=p(-1)=13 / 55 \\
p(2)=p(-2)=1 / 11 ; p(3)=p(-3)=1 / 165
\end{array}$$
Compute the conditional probability that the gambler wins $i, i=1,2,3,$ given that he wins a positive amount.

Added by Samantha M.

Probability with Applications in Engineering, Science, and Technology

Matthew A. Carlton • Jay L. Devore 2nd Edition

Instant Answer

Solved by Expert Ramesh Rajak

11/29/2021

Step 1

Given that $P(1) = P(-1) = \frac{13}{55}$ and $P(2) = P(-2) = \frac{1}{11}$, we have: $$P(A) = P(1) + P(2) = \frac{13}{55} + \frac{1}{11} = \frac{39}{55}$$ Show more…

Show all steps

Thanks for your feedback!

Let $X$ be the winnings of a gambler. Let $p(i)=$ $P(X=i)$ and suppose that $$\begin{array}{l} p(0)=1 / 3 ; p(1)=p(-1)=13 / 55 \\ p(2)=p(-2)=1 / 11 ; p(3)=p(-3)=1 / 165 \end{array}$$ Compute the conditional probability that the gambler wins $i, i=1,2,3,$ given that he wins a positive amount.