Correct Answer - C
Let the coin be tossed n times and let X-denote the number of heads in n tosses of the coin. Then,
∴P(X=r)=.nCr(
1
2
)r(
1
2
)n-r=.nCr(
1
2
)n,r=0,1,2...n
It is given that
P(X≥2)≥0.96
⇒
n
∑
r=2
P(X=r)≥0.96
⇒
n
∑
r=2
.nCr(
1
2
)n≥0.96
⇒
1
2n
(
n
∑
r=2
.nCr)≥0.96
⇒
1
2n
(2n-.nC0-.nC1)≥0.96
⇒1-
n+1
2n
≥(0.04)2n
⇒n=8,9,10,...
Hence the least value of n is 8.
