Question

a bag has 5 white and 3 black balls. four balls are drawn in succession with replacement. find the probability that they are alternately of different colours.

Answer 1

The probability that the balls drawn are alternately of different colors is 15/32.

Step-by-step explanation:

To find the probability that the balls drawn are alternately of different colors, we need to consider the different possible outcomes.

Out of the 8 balls in the bag, there are 5 white and 3 black. When drawing 4 balls with replacement, there can be 2 possible outcomes:

1. The first ball drawn is white and the second ball drawn is black.
2. The first ball drawn is black and the second ball drawn is white.

For the first outcome, the probability is (5/8) * (3/8). For the second outcome, the probability is (3/8) * (5/8). Therefore, the total probability is (5/8) * (3/8) + (3/8) * (5/8) = 30/64 = 15/32.