A person throws two fair dice.
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 :

1. 2 gain

2. $\frac{1}{2}$ loss

3. $\frac{1}{4}$ loss

4. $\frac{1}{2}$ gain

Correct Option: , 2

Solution:

win Rs.15 $\rightarrow$ number of cases $=6$

win Rs.12 $\rightarrow$ number of cases $=4$

loss Rs. $6 \rightarrow$ number of cases $=26$

$\mathrm{p}($ expected gain $/$ loss $)=15 \times \frac{6}{36}+12 \times \frac{4}{36}$

$6 \times \frac{26}{36}=-\frac{1}{2}$