Question

In a purse there are $10$ coins, all shillings except one which is a sovereign; In another, there are ten coins all shillings. Nine coins are taken from the former purse and put into the latter, and then nine coins are taken from the latter and put into the former: find the chance that the sovereign is still in the first purse.

Answer 1

For the sovereign to be in the second purse, two conditions needs to be met

1) The sovereign was among the 9 coins moved to the second purse

2) The sovereign not among the 9 coins moved again to the first purse

Probability of (1) happening is $\frac{9}{10}$ and the probability of (2) happening is $\frac{10}{19}$

$\therefore$ Probability of both happeing $=\frac{9}{10}\times \frac{10}{19}=\frac{9}{19}$

$\therefore$ Probability that the sovereign is in the first purse $=1-\frac{9}{19}=\frac{10}{19}$