Question

The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least 0.96 is :
A. 7
B. 9
C. 8
D. 5

Answer 1

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,
`therefore P(X=r)= .^(n)C_(r )((1)/(2))^(r )((1)/(2))^(n-r) = .^(n)C_(r )((1)/(2))^(n), r=0,1,2,..,n`
It is given that
`P(X ge 2) ge 0.96`
`implies underset(r=2)overset(n)(sum)P(X=r) ge 0.96`
`implies underset(r=2)overset(n)(sum) .^(n)C_(r )((1)/(2))^(n) ge 0.96`
`implies (1)/(2^(n))( underset(r=2)overset(n)(sum) .^(n)C_(r )) ge 0.96`
`implies (1)/(2^(n)) (2^(n) - .^(n)C_(0) - .^(n)C_(1)) ge 0.96`
`implies 1-(n+1)/(2^(n)) ge 0.96`
`implies (n+1) le (0.04) 2^(n)`
`implies n=8, 9, 10,`..