Q98 / 150 · MHT CET 2016 · Mathematics

If random variable $X \sim B (n = 5, p = \frac{1}{3})$ then $P (2 < X < 4) =$

A
$\frac{80}{243}$
Correct answer
B
$\frac{40}{243}$
C
$\frac{40}{343}$
D
$\frac{80}{343}$

Solution

Given

n = 5

p = \frac{1}{3}

∴ q = \frac{2}{3}

P (2 < x < 4) = P (x = 3)

=^{5} C_{3} {(\frac{1}{3})}^{3} {(\frac{2}{3})}^{2}

= \frac{5 \times 4}{2} \times \frac{1}{27} \times \frac{4}{9}

= \frac{40}{243}

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

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