Question

Mother, Father and son line up at random for a family picture. Find P(A/B), if A and B are defined as follows:

A = Son on one end
B = Father in the middle

Answer 1

To find the probability of the son (event A) being on one end when the father (event B) is in the middle, we look at the likelihood of A given B. There are 2 possible arrangements for A to occur given B, therefore P(A|B) is 1. The correct answer is that A and B are 'Neither mutually exclusive nor independent'.

Step-by-step explanation:

The probability of event A, which is the son being on one end, given event B, the father being in the middle, can be calculated using conditional probability. To find the P(A|B), we need to consider the number of favorable outcomes for A when B is already occurring. Given that the father is in the middle, there are two possible positions for the son to be on an end, so the probability is 2 out of the 2 possible arrangements for the remaining positions. Therefore, P(A|B) is 1. As for the options listed:

• Mutually exclusive
• Independent
• Mutually exclusive and independent
• Neither mutually exclusive nor independent

Option D, 'Neither mutually exclusive nor independent,' would be considered the correct choice here because the events can occur together, and the occurrence of B affects the probability of A.