There are 3 black and 4 blue balls are in bag 1 and 6 blue and 2 black balls are in bag 2. If a ball is drawn from each bag, then find the probability of both balls are black.

Correct option is B

Probability Solution

We are given two bags containing black and blue balls:

Bag 1: 3 black and 4 blue balls → Total = 3 + 4 = 7

Bag 2: 2 black and 6 blue balls → Total = 2 + 6 = 8

We randomly pick one ball from each bag. We need to find the probability that both drawn balls are black.

Step 1: Compute Individual Probabilities

Probability of drawing a black ball from Bag 1:

​$$P(B_1) = \frac{\text{Black balls in Bag 1}}{\text{Total balls in Bag 1}} = \frac{3}{7}$$​

Probability of drawing a black ball from Bag 2:

​$$P(B_2) = \frac{\text{Black balls in Bag 2}}{\text{Total balls in Bag 2}} = \frac{2}{8} = \frac{1}{4}$$​

Step 2: Compute the Combined Probability

Since the selections from each bag are independent, we multiply the individual probabilities:

$$P(\text{Both black}) = P(B_1) \times P(B_2) = \frac{3}{7} \times \frac{1}{4} = \frac{3}{28}$$​

​$$\frac{3}{28}$$​