Question

A bag contains $6$ white and $4$ red balls. If a person draws $2$ balls and receives Rs. $10$ and Rs. $20$ for a white and red balls respectively, then his expected amount is -

• A. Rs. $25$
• B. Rs. $26$
• C. Rs. $29$
• D. Rs. $28$

Answer 1

Answer: (D)

Rs. $28$

A bag contains $6$ white and $4$ red balls.

A white ball drawn then $Rs10$

If red ball then $Rs20$

$\Rightarrow$ Expectation $=2(n_1{P}_1+n_2{P}_2)$

Here $P_1=$ Probability of getting a white ball

$=\frac{{}^6{C}_1}{{}^{10}{C}_1}=0.6$ $n_1=Rs10$

Here $P_2=$ Probability of getting a red ball

$=\frac{{}^4{C}_1}{{}^{10}{C}_1}=0.4$ $n_2=Rs20$

$\therefore$ Expectation $=2[0.6\times 10+0.4\times 20]$

$=Rs28.$

Hence, the answer is Rs.$28.$