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

Answer 1

1 - P(no head) - P(one head) $≥\, 0.96$
$1-\,{}^{n}C_{0} \left(\frac{1}{2}\right)^{n} - \,{}^{n}C_{1} \left(\frac{1}{2}\right)^{n} \ge 0.96$
$\frac{n+1}{2^{n}} \le 0.04$
$\frac{n+1}{2^{n}} \le \frac{1}{25}$
Minimum value of n is 8.