Question

A box contains 5 red balls and 3 black balls. If two balls are picked up randomly from the box, determine the following: (i) The probability that the second ball is red.

Answer 1

The probability that the second ball drawn is red is 35/64.

Step-by-step explanation:

To find the probability that the second ball is red, we need to consider two scenarios. In the first scenario, we assume that the first ball picked is not red. In this case, there are 3 black balls and 5 red balls left in the box. So the probability of picking a red ball for the second pick is 5/8.

In the second scenario, we assume that the first ball picked is red. In this case, there are 4 red balls and 3 black balls left in the box. So the probability of picking a red ball for the second pick is 4/7.

Now, we need to consider the probabilities of these two scenarios happening. The probability of picking a non-red ball first is 3/8 and the probability of picking a red ball first is 5/8. So the overall probability of the second ball being red is:

(3/8) * (5/8) + (5/8) * (4/7) = 15/64 + 20/56 = 35/64