Q. 15  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

                In the following, choose the correct answer:

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

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

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

                (D)  None of these

Answers (1)

Let X represent number students out of 5 who are swimmers.

Probability of student who are not swimmers =q

        q=\frac{1}{5}

        P=1-q=1-\frac{1}{5}=\frac{4}{5}

X has a binomial distribution,n=5

\therefore \, \, \, \, P(X=x)=^nC_x.q^{n-x}.p^x

                P(X=x)=^5C_x.(\frac{1}{5})^{5-x} . (\frac{4}{5})^{x}

                    P(4\, \,students\, \, are\, swimmers)=P(X= 4)

                                                                                          =^5C_4(\frac{1}{5})^{1} . (\frac{4}{5})^{4}

Option A is correct.

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