Question

A had in his pocket a sovereign and four shillings; taking out two coins at random he promises to give them to $B$ and $C$. What is the worth of $C^{\prime }s$ expectation?

Answer 1

He can either draw two shillings or one shilling and one sovereign

We know $1$ sovereign $=$ $20$ shillings

Expectation of $B$ and $C$ in first case $=\frac{1}{2}(\frac{{}^4{C}_2}{{}^5{C}_2}\times 2)=\frac{3}{5}$

Expectation of $B$ and $C$ in second case $=\frac{1}{2}(\frac{{}^4{C}_1{\times }^1{C}_1}{{}^5{C}_2}\times 21)=\frac{21}{5}$

$\therefore$ total expectation $=\frac{21}{5}+\frac{3}{5}=\frac{24}{5}$