Question

A purse contains $10$ ten rupee coins and $5$ five rupee coins. Two coins are randomly drawn. If the expected value of $2$ drawn coins is $λ,$ then $3λ$ is equal to

Answer 1

Answer: 50

$2$ coins can be both $10$ rupee coins, both $5$ rupee coins or one $5$ rupee coin and one $10$ rupee coin
So, expected value
$=\frac{{}^{10}{C}_2}{{}^{15}{C}_2}×20+\frac{{}^5{C}_2}{{}^{15}{C}_2}×10+\frac{{}^{10}{C}_1^5{C}_1}{{}^{15}{C}_2}×15$ $=\frac{3}{7}×20+\frac{2}{21}×10+\frac{10}{21}×15$
$=\frac{350}{21}=\frac{50}{3}$
i.e. $λ=\frac{50}{3}$
Hence, $3λ=50$