Question

A person throws two fair dice. He wins Rs. $15$ for throwing a doublet (same numbers on the two dice), wins Rs. $12$ when the throw results in the sum of $9$, and loses Rs. $6$ for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is :

• A. $2$ gain
• B. $\frac{1}{2}$ loss
• C. $\frac{1}{2}$ gain
• D. $\frac{1}{4}$ loss

Answer 1

The correct option is B $\frac{1}{2}$ loss

$\begin{array}{cccc}X& +15& +12& -6\\ P\left(X\right)& \frac{1}{6}& \frac{1}{9}& \frac{13}{18}\end{array}$

$E\left(X\right)=15\times \frac{1}{6}+12\times \frac{1}{9}-6\times \frac{13}{18}=-\frac{1}{2}$
So, expection is $\frac{1}{2}$ with a loss