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Question

A coin is tossed n times. The probability of getting at least once is greater than 0.8. Then, the least value of n, is
(a) 2
(b) 3
(c) 4
(d) 5

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Solution

(b) 3

Let X be the number of heads. Then X follows a binomial distribution with

p =12, q=12Hence, the distribution is given by P(X=r) = Crn12r12n-r, r=0,1,2,3......nP(X1) =1-P(X=0) = 1-12n 0.8Or 2n10.2 2n5This is possible only when n 3.So, the least value of n must be 3.

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