Question

The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least 0.96 is : Select the correct answer from above options

Answer 1

Using Binomial distribution, `P(Xge2)=1-P(X=0)-P(x=1)` `=1-((1)/(2))^(n)-[overset(n)C_(1).((1)/(2)).((1)/(2))^(n-1)]` `=1-(1)/(2^(n))-overset(n)""C_(1).(1)/(2^(n))=1-((1+n)/(2^n))` Given, `P(Xge2)ge0.96` `:. 1-((n+1))/(2^(n))ge(24)/(25)` `rArr (n+1)/(2^(n))le(1)/(25)` `:. n=8`