Question

What is the chance of drawing a sovereign from a purse one compartment of which contains $3$ shillings and $2$ sovereigns, and the other $2$ sovereigns and $1$ shilling?

Answer 1

probability of selecting first compartment $=\frac{1}{2}$

Now probability of drawing a sovereign$=\frac{2}{5}$

$\Rightarrow$ probability of drawing sovereign from the first compartment $=\frac{1}{2}\times \frac{2}{5}=\frac{1}{5}$

probability of selecting second compartment $=\frac{1}{2}$

Now probability of drawing a sovereign$=\frac{2}{3}$

$\Rightarrow$ probability of drawing sovereign from the second compartment $=\frac{1}{2}\times \frac{2}{3}=\frac{1}{3}$

So probability of drawing a sovereign from the purse $=\frac{1}{5}+\frac{1}{3}=\frac{8}{15}$