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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 (a) at least 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

               (a) at least once

Answers (1)

best_answer

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 \:at\: least\: once)=P(X\geq 1)

                                                                      =1-P(X< 1) 

                                                                      =1-P(X= 0)

                                                                      =1- ^{50}C_0 (\frac{99}{100})^{50}

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

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

Posted by

seema garhwal

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