Question

there are two bags. the first bag contains 5 white and 3 black balls and the second bag contains 3 white and 5 black balls. two balls are drawn at random from the first bag and are put into the second bag without noticing their colors. then two balls are drawn from the second bag. find the probability that the balls are white.

Answer 1

The probability that the balls drawn from the second bag are white is 28/91.

Step-by-step explanation:

To find the probability that the balls drawn from the second bag are white, we need to consider all the possible outcomes.

Let's break it down step by step:

Step 1: Calculate the probability of drawing 2 white balls from the first bag.

Probability of drawing 2 white balls from the first bag = (5/8) * (4/7)

= 20/56

= 5/14

Step 2: Calculate the probability of drawing white balls from the second bag after adding the 2 balls from the first bag without noticing their colors.

Probability of drawing 2 white balls from the second bag = (8/14) * (7/13)

= 56/182

= 28/91

So, the probability that the balls drawn from the second bag are white is 28/91.