Question

Ten married couples are seated randomly in a circle. Find the expected number of wives sitting next to their husbands.

a) 1/2
b) 2/3
c) 1/3
d) 3/4

Answer 1

The expected number of wives sitting next to their husbands is 512.

Step-by-step explanation:

To find the expected number of wives sitting next to their husbands, we need to calculate the probability that a wife sits next to her husband for each couple. In a circle, there are 2 possible ways for a wife to sit next to her husband: either on his left or on his right. There are 10 couples, so the total number of possibilities is 2^10 = 1024. Therefore, the expected number of wives sitting next to their husbands is 1024/2 = 512.

Answer: The expected number of wives sitting next to their husbands is 512.