Question

There are $3$ coins in a box. The probability of getting head is $\frac{2}{3}$ for two of them, while for remaining it is $\frac{1}{2}$. A coin is chosen at random and tossed $3$ times, showing head in each case. What is the probability that the coin is unbiased ?

Answer 1

P(biased coin)$=\frac{2}{3}$

P(unbiased coin)$=\frac{1}{2}$

P(unbiased & head)$=\frac{2}{3}$

P(biased & head)$=\frac{1}{2}$

P(coin is unbiased)$=\frac{\frac{1}{2}\times \frac{1}{2}}{\frac{1}{2}\times \frac{1}{2}+\frac{2}{3}\times \frac{2}{3}}$

$=\frac{9}{25}$.