Question

Find 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 $0.96$

Answer 1

Let the coin be tossed $n$ times

$P\left(leastvalueheads\right)=1-{\left(\frac{1}{2}\right)}^n{-}^n{C}_2{\left(\frac{1}{2}\right)}^n\ge 0.96$

$\Rightarrow \frac{4}{100}\ge \frac{n+1}{2^n}$

$\Rightarrow \frac{n+1}{2^n}\le \frac{1}{25}$

$\Rightarrow \frac{2^n}{n+1}\ge 25$

$\therefore$ least value of $n$ is $8$