Minimum number of times a fair coin must be tossed so that the probility of gettig atleast one head is more than `99%` is

Options

A. 8
B. 6
C. 7
D. 5

Answer

C

Explanation

As we know probability of getting a head on a toss of a fair coin is `P(H)=(1)/(2)=p(let)`
Now, let n be the minimum numbers of toss required to get at least one head, then required probability =1-(probability that on all 'n' toss we are getting tail )
`=1-((1)/(2))^(n)" " [:' P(tail)=P("Head")=(1)/(2)]`
According to the question,
`1-((1)/(2))^(n)gt(99)/(100) rArr((1)/(2))^(n)lt1-(99)/(100)`
`rArr ((1)/(2))^(n)lt(1)/(100)rArr 2^(n)gt100`
`rArr " " n=7 " "`[for minimum]