First slide

Random variable and probability distribution

Question

The probability that a student is a swimmer is $\frac{4}{5}$ . The probability that out of 5 students exactly 2 are swimmers is

Moderate

A

${(\frac{4}{5})}^{3}$
B

${(\frac{4}{5})}^{4}$
C

$\frac{2^{5}}{5^{4}}$
D

$(\frac{4}{5}) {(\frac{1}{5})}^{4}$

Solution

$p = \frac{4}{5}, q = \frac{1}{5}, n = 5$
$p (X = 2) =^{5} C_{2} {(\frac{1}{5})}^{3} {(\frac{4}{5})}^{2} = \frac{2^{5}}{5^{4}}$

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