The probability that a student is not a swimm | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The selection of students who are swimmers follows a binomial distribution. Let $X$ be the number of students who are swimmers out of $n=5$ studen

Vedclass · Accepted Answer

$^{5}C_{4} \left(\frac{4}{5}\right)^{4} \left(\frac{1}{5}\right)$

Vedclass · Answer

(A) The selection of students who are swimmers follows a binomial distribution. Let $X$ be the number of students who are swimmers out of $n=5$ students.The probability that a student is not a swimmer is $q = \frac{1}{5}$.The probability that a student is a swimmer is $p = 1 - q = 1 - \frac{1}{5} = \frac{4}{5}$.The probability distribution is given by $P(X=x) = ^{n}C_{x} p^{x} q^{n-x}$.For $n=5$ and $x=4$,we have:$P(X=4) = ^{5}C_{4} \left(\frac{4}{5}\right)^{4} \left(\frac{1}{5}\right)^{5-4} = ^{5}C_{4} \left(\frac{4}{5}\right)^{4} \left(\frac{1}{5}\right)$.Thus,the correct option is $A$.

The probability that a student is not a swimmer is $\frac{1}{5}$. Then the probability that out of five students,four are swimmers is

Similar Questions

If $X$ has a binomial distribution with mean $np$ and variance $npq$,then $\frac{P(X = k)}{P(X = k - 1)}$ is

$A$ fair coin is tossed a fixed number of times. If the probability of getting exactly $3$ heads equals the probability of getting exactly $5$ heads, then the probability of getting exactly one head is

The probability that a bulb produced by a factory will fuse after $150$ days of use is $0.05$. Find the probability that out of $5$ such bulbs,at least one will fuse after $150$ days.

$A$ die is thrown $6$ times. If 'getting an odd number' is a success,what is the probability of at most $5$ successes?

$A$ dice is thrown $10$ times. If getting an even number is considered as a success,then the probability of $4$ successes is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module