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Question

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


Solution


He lost $$13$$ times out of $$14$$ 
Probability of winning or losing a toss  is
$$\dfrac{1}{2}$$.
The coin is thrown $$14$$ successive times He loses $$13$$ times
so the probability $$13$$ times 
$$\underset{13\,out\, of\,14\,tosses}{^{14}C_{13}}\times \underset{losing\,13\,times}{(\dfrac{1}{2})^{13}}\times \underset{winning\, 1\,times}{(\dfrac{1}{2})^1}$$
So, $$P=14\times (\dfrac{1}{2})^{14}$$
$$=14\times \dfrac{1}{128}\times \dfrac{1}{128}$$
$$=\dfrac{7}{64\times 128}=\dfrac{7}{8192}$$

Maths

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