The minimum number of times one has ot toss a fair coin so that the probability of observing atleast one head is atlest `90%` is

Options

A. 2
B. 3
C. 5
D. 4

Answer

D

Explanation

The required probability of observing atleast one head
`=1-p(no head)`
`=1-(1)/(2^(n))" "` [let number of toss are n]
`[:' P("Head")=p(Tail)=(1)/(2)]`
According to the question, `1-(1)/(2^(n))ge(90)/(100)`
`rArr (1)/(2^(n))le(1)/(20)rArr 2^(n)ge10 rArrnge4`
so, minimum number of times one has to toss a fair coin so that the probability of observing atleast one head is atleast 90% is 4.