about to only mathematics

Options

A. 7
B. 9
C. 8
D. 5

Answer

C

Explanation

Let the coin be tossed n times and let X-denote the number of heads in n tosses of the coin. Then,
`thereforeP(X=r)=.^nC_(r)((1)/(2))^r((1)/(2))^(n-r)=.^nC_(r)((1)/(2))^n,r=0,1,2...n`
It is given that
`P(Xge 2)ge 0.96`
`rArr sum_(r=2)^(n)P(X=r)ge 0.96`
`rArr sum _(r=2)^(n).^nC_(r)((1)/(2))^nge 0.96`
`rArr (1)/(2^n)(sum_(r=2)^(n).^nC_(r))ge 0.96`
`rArr (1)/(2^n)(2^n-.^nC_(0)-.^nC_(1))ge 0.96`
`rArr 1-(n+1)/(2^n)ge (0.04)2^n`
`rArr n=8,9,10,...`
Hence the least value of n is 8.