Question

A boy tosses fair coin $3$ times. If he gets $Rs.2X$ for $X$ heads then his expected gain equals to $Rs$

• A. $1$
• B. $\frac{3}{2}$
• C. $3$
• D. $4$

Answer 1

Answer: (C)

$3$

For $x$ heads, he gets $y=2x$ Rs.

$x$	$0$	$1$	$2$	$3$
$y$	$0$	$2$	$4$	$6$
$p\left(y\right)$	$\frac{1}{8}$	$\frac{3}{8}$	$\frac{3}{8}$	$\frac{1}{8}$

Expected gain $=\sum y_i{p}_i$

$=0\left(\frac{1}{8}\right)+2\left(\frac{3}{8}\right)+4\left(\frac{3}{8}\right)+6\left(\frac{1}{8}\right)=\frac{6+12+6}{8}=3$