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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 (c) at least twice?

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

                (c) at least twice?

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 \, \, twice)=P(X\geq 2)

                                                                      =1-P(X< 2) 

                                                                      =1-P(X\leq 1)

                                                                      =1-(P(X=0)+P(X=1))

                                                                      =1- (\frac{99}{100})^{50}-\frac{1}{2}(\frac{99}{100})^{49}

                                                                      =1- (\frac{99}{100})^{49}(\frac{1}{2}+\frac{99}{100})

                                                                      =1- (\frac{99}{100})^{49}\frac{149}{100}

Posted by

seema garhwal

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