Question

How many times must a man toss a fair com so that the probability of having at least one head is more than 90%? Select the correct answer from above options

Answer 1

Let `n` times a coin must be tossed so that probablity of having at least one head is more than `90%`. `P(`At least one head`) = 1-P(`All tail`)` `=>1-(1/2)^n > 90/100` `=>(1/2)^n >=0.1` Adding log base 10, to both sides, `n(log1 - log2) > -1` `-nlog2 > -1` `n>1/log2=>n >1/0.3=>n>3.33` So, coin must be tossed at least 4 times so that probablity of having at least one head is more than `90%`.