The probability that a student is not a swimmer is $1 / 5$. Then the probability that out of five students, four are swimmers is A. ${ }^{5} \mathrm{C}{4} 1 / 5(4 / 5)^{4}$ B. $(4 / 5)^{4}(1 / 5)$ C. ${ }^{5} \mathrm{C}{1} 1 / 5(4 / 5)^{4}$ D. None of these

Home » The probability that a student is not a swimmer is . Then the probability that out of five students, four are swimmers is A. B. C. D. None of these

The probability that a student is not a swimmer is $1 / 5$ . Then the probability that out of five students, four are swimmers is
A. ${ }^{5} \mathrm{C}{4} 1 / 5(4 / 5)^{4}$
B. $(4 / 5)^{4}(1 / 5)$
C. ${ }^{5} \mathrm{C}{1} 1 / 5(4 / 5)^{4}$
D. None of these

CBSE | Class 12 | Maths | NCERT | Probability

The probability that a student is not a swimmer is $1 / 5$ . Then the probability that out of five students, four are swimmers is
A. ${ }^{5} \mathrm{C}{4} 1 / 5(4 / 5)^{4}$
B. $(4 / 5)^{4}(1 / 5)$
C. ${ }^{5} \mathrm{C}{1} 1 / 5(4 / 5)^{4}$
D. None of these

Solution:
Answer: A. ${ }^{5} \mathrm{C}_{4} 1 / 5(4 / 5)^{4}$

Explanation:

Assume that $X$ is the number of pupils who are swimmers out of a class of five. The Bernoulli trials are also used to select students who are swimmers on a regular basis. As a result, the likelihood of kids who are not swimmers $=\mathrm{q}=1 / 5$

Clearly, we have $\mathrm{X}$ has the binomial distribution where $\mathrm{n}=5$

And, $p=1-q$

$=1-1 / 5$

$=4 / 5$

$\therefore P(X=x)={ }^{n} C_{x} q^{n-x} p^{x}$

$={ }^{5} C_{x}\left(\frac{1}{5}\right)^{5-x} \cdot\left(\frac{4}{5}\right)^{x}$

Hence, probability that four students are swimmers $=\mathrm{P}(\mathrm{X}=4)$
$={ }^{5} C_{4}\left(\frac{1}{5}\right) \cdot\left(\frac{4}{5}\right)^{4}$