Question

A bag contains a very large number of white and black marbles in the ratio 1 : 2. Two samples of marbles, 5 each are picked up. The probability that the first sample contains exactly one black and the second exactly three marbles is

• A. $\frac{10}{3^9}$
• B. $\frac{1600}{3^{10}}$
• C. $\frac{800}{3^{10}}$
• D. $\frac{10}{3^5}$

Answer 1

Answer: (C)

$\frac{800}{3^{10}}$

Since there are large no. of marbles present, therefore we will not consider any change in bag even after drawing 10 marbles

Probability of drawing black marble = 2/3

Probability of drawing white marble = 1/3

Required Probability = ${}^5{C}_1$*$({\frac{2}{3})}^1\times {\left(\frac{1}{3}\right)}^4$*${}^5{C}_2$*${\left(\frac{2}{3}\right)}^2\times {\left(\frac{1}{3}\right)}^3$