The probability that a student is not a bowler is $\frac{1}{5}$. Then, the probability that out of the five students four are bowlers is:
Answer & explanation
Correct answer: option 4
A = No. of students who are bowler out of 5 = 4
Probability that a student is not a bowler is (q) = \(\frac{1}{5}\)
Probability that a student is a bowler is (p) = 1 - Probability that a student is not a bowler
Probability that a student is a bowler is (p) = 1 - \(\frac{1}{5}\) = \(\frac{4}{5}\)
Binomial distribution of A P(A = a) = nCa qn-a pa
P(A = ) = 5C4 q1 p4
= ${ }^5 C_4\left(\frac{1}{5}\right)\left(\frac{4}{5}\right)^4$
The correct answer is Option (4) → ${ }^5 C_4\left(\frac{1}{5}\right)\left(\frac{4}{5}\right)^4$