First slide

Random variable and probability distribution

Question

The probability that a student is not a swimmer is $1 / 5 .$ The probability that out of $5$ students exactly $4$ are swimmer is

Moderate

A

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

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

$^{5} C_{4} {(\frac{4}{5})}^{4}$
D

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

Solution

Let $p =$ probability that a student selected at random is a swimmer
$= 1 - 1 / 5 = 4 / 5$ .
$n =$ number of students selected $= 5$
and $X =$ number of swimmers
Then $X ~ B (n, p)$ where $n = 5$ and $p = 4 / 5$
Probability that exactly $4$ students are swimmer is
$=^{5} C_{4} p^{4} q = 5 {(\frac{4}{5})}^{4} (\frac{1}{5}) = {(\frac{4}{5})}^{4} .$

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