Question

South African cricket captain lost the toss of a coin $13$ times out of $14$. The chance of this happening was ____

Answer 1

He lost $13$ times out of $14$

Probability of winning or losing a toss is

$\frac{1}{2}$.

The coin is thrown $14$ successive times He loses $13$ times

so the probability $13$ times

$\underset{13outof14tosses}{{}^{14}{C}_{13}}\times \underset{losing13times}{(\frac{1}{2}{)}^{13}}\times \underset{winning1times}{(\frac{1}{2}{)}^1}$

So, $P=14\times (\frac{1}{2}{)}^{14}$

$=14\times \frac{1}{128}\times \frac{1}{128}$

$=\frac{7}{64\times 128}=\frac{7}{8192}$