Q68 / 150 · MHT CET 2017 · Mathematics

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

A
$1$
B
$\frac{3}{2}$
Correct answer
C
$3$
D
$4$

Solution

For

x

heads, he gets

y = 2 x

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

Excepted gain

= \sum y_{i} p_{i}

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

Hence, the correct answer is option: 'C'.

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