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Question

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning prize is 1100. What is the probability that he will win a prize.
atleast twice ?

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Solution

Let X denotes the number of times that the person wins the prize, Here, it is a case of Bernoulli trails with n=50, p=1/100 and q=1-p=1-1100=99100.
P(X=r)=nCrprqnr=50Cr(1100)r.(99100)50r

P (he wins atleast twice)= P(X2)=1P(X=0,1)=1[P(0)+P(1)]
=1(50C0p0q50+50C1p1q49)=1(q50+50pq49)

=1q49(p+50p)=1(99100)49 (99100+50×1100)=1149100(99100)49


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