Question

Suppose there are 6 white and 5 black marbles in a bag and you want to select 2 marbles. What is the probability that you will select a white marble then a black marble? You will replace the white marble. [give your answer to 4 d.p.]

Answer 1

Total number of marbles = 6+5=11

The probability of selecting white marble is

$P(white) = \frac{6}{11}$

Since the marble is replaced, so total number of marbles will remain same.

So, the probability of selecting black marble is

$P(black) = \frac{5}{11}$

Therefore, the probability of selecting a white marble then a black marble with replacement is calculated as follows:

$P(white \; then \; black) = P(white) \times P(black) \\ = \frac{6}{11} \times \frac{5}{11} \\ = \frac{30}{121} =0.2479$