A person throws two fair dice. He wins Rs. , 15 for throwing a do… - Vidyadip

MCQ

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
$\frac{1}{4}$ loss
B
$2$ gain
C
$\frac{1}{2}$ gain
✓
$\frac{1}{2}$ loss

✓

Answer

Correct option: D.

$\frac{1}{2}$ loss

d

$Coin$	$+15$	$+12$	$-6$
$Probability$	$\frac{6}{{36}}$	$\frac{4}{{36}}$	$\frac{{26}}{{36}}$

Probability of doublet $=\frac{6}{36}$

Probability of sum of $9=\frac{4}{36}$

Other probability $=\frac{26}{36}$

Expected gain/loss $=15 \times \frac{6}{36}+12 \times \frac{4}{36}-6 \times \frac{26}{36}$

$=\frac{90}{36}+\frac{48}{36}-\frac{156}{36}=\frac{-1}{2}$

Hence correct answer is option $(D)$

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