The least number of times a fair coin must be tossed so that the probability of getting atleast one head is atleast 0.8 is

Step-by-step solution

Suppose the coin is tossed n times. Let X be the number of the heads obtained. Then, X follows a binomial distribution with parameters n and p= 1 2 Now, P(X 1) 0.8 1-P(X=0) 0.8 1- ^n C₀ p^0(1-p)^n 0.8 ( 1 2 )^n 0.2 or ( 1 2 )^n 1 5 2^n 5 n 3 Hence, the least value of n is 3 .