Question

Out of ten coins, one of the coin is known to have heads on both sides. He takes out one coin at random and tosses it $5$ times. If it always falls with head upwards, the probability that it is double headed coin is

Answer 1

P(double headed $=\frac{1}{10}$

P(Normal)$=\frac{9}{10}$

$P\left(\frac{Head}{Normal}\right)=\frac{1}{2}$

$P\left(\frac{Head}{doubleheaded}\right)=1$

P(coin is D.H)$=\frac{\frac{1}{10}{{}^{5}C}_5{\left(1\right)}^5}{\frac{1}{10}{{}^{5}C}_5{\left(1\right)}^5+\frac{9}{10}{{}^{5}C}_5{\left(\frac{1}{2}\right)}^5}$

$=\frac{\frac{1}{10}}{\frac{1}{10}+\frac{9}{320}}=\frac{320}{410}=\frac{32}{41}$