A coin is tossed n times. The probability of getting head atleast once is greater than 0.8. Then the least value of such n is

Options

A. 7
B. 6
C. 5
D. 3

Answer

D

Explanation

Suppose the coin is tossed n times. Let X be the number of heads obtained. Then, X follows a binomial distribution with parameters n and `p=1//2`.
Now,
`P(Xge1)ge0.8`
`rArr 1-P(X=0)ge0.8`
`rArr 1-.^nC_(0)p^0(1-p)^nge 0.8`
`rArr ((1)/(2))^nle 0.2rArr ((1)/(2))^nle (1)/(5)rArr 2^nge 5rArr nge 3`
Hence, the least value of n is 3.