Question

A purse contains of four coins; two coins having been drawn are found to be sovereigns: find the chance $\left(1\right)$ that all the coins are sovereigns, $\left(2\right)$ that if the coins are replaced another drawing will give a sovereign.

Answer 1

There are $3$ equally likely hypothesis; for the purse may contain $2,$ or $3$ or $4$ sovereign

Now, $P_1=\frac{1}{6},P_2=\frac{1}{2},P_3=1,$

$\therefore$ The chance that all are sovereigns

$=\frac{P_1}{\sum P}=\frac{3}{5}$

Again, $\frac{P_1}{1}=\frac{P_2}{3}=\frac{P_3}{6}=\frac{\sum P}{10}$

$\therefore Q_1=\frac{1}{10}.Q_2=\frac{3}{10},Q_3=\frac{6}{10}$

$\therefore$ The chance that another drawing will give a sovereign

$=Q_1\times \frac{1}{2}+Q_2\times \frac{3}{4}+Q_3\times 1$

$=\frac{1}{20}+\frac{9}{40}+\frac{6}{10}=\frac{7}{8}$