Question

There are two bags, one of which contains 3 black balls and 4 white balls, while the other contains 4 black and 3 white balls, a fair die is cast, if the face 1 or 3 turns up, a ball is taken from the first bag, and if any other face turns up, a ball is chosen from the second bag. find the probability of choosing a black ball

a. 1/3
b.11/21
c.2/3
d.10/21

Answer 1

The probability of choosing a black ball is option A) 1/3.

Step-by-step explanation:

To calculate the probability of choosing a black ball, we need to consider the probabilities of choosing from each bag based on the outcome of rolling a fair die.

There are two bags, Bag 1 with 3 black balls and 4 white balls, and Bag 2 with 4 black balls and 3 white balls.

If a 1 or 3 is rolled, a ball is taken from Bag 1. If any other face turns up, a ball is chosen from Bag 2.

The probability of rolling a 1 or 3 is 2/6, while the probability of rolling any other face is 4/6.

So, the overall probability of choosing from Bag 1 is (2/6) * (3/7), since there are 2 favorable outcomes out of 6 and 3 black balls out of a total of 7 balls in Bag 1.

Similarly, the probability of choosing from Bag 2 is (4/6) * (4/7), since there are 4 favorable outcomes out of 6 and 4 black balls out of a total of 7 balls in Bag 2.

Therefore, the total probability of choosing a black ball is:

(2/6) * (3/7) + (4/6) * (4/7) = 1/3