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A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is 1/100. What is the probability that he will win a prize (b) exactly once

Q. 10  A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is \frac{1}{100}. What is the probability that he will win a prize

                (b) exactly once

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Let X represent number of winning prizes in 50 lotteries .

        P=\frac{1}{100}

        q=1-P=1-\frac{1}{100}=\frac{99}{100}

X has a binomial distribution,n=50.

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

                P(X=x)=^50C_x.(\frac{1}{100})^{50-x} . (\frac{99}{100})^{x}

                    P(winning\, exactly\, once)=P(X= 1)

                                                                      =^{50}C_1 (\frac{99}{100})^{49}.\frac{1}{100}

                                                                      = 50.(\frac{99}{100})^{49}\frac{1}{100}

                                                                      =\frac{1}{2} (\frac{99}{100})^{50}

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