Two married couples have purchased theater tickets and are seated in a row consisting of just 4 seats. If they take their seats
in a completely random order, what is the probability that at least one of the wives ends up sitting next to her husband? Hint: Use probability of a complement event. That is, P(A) = 1 − P(A′), where A′ is the complement of an event A.
To use probability of a complement event, we need to find the situation where none of the couples are sitting next to each other which can happen either two husbands are sitting in the seats 2 and 3 or two wives are sitting in the seats 2 and 3. Also in the first scenario, the wives would need to be sitting at the opposite ends to their husbands and vice versa for the second scenario.
So there are in total 4 scenarios where no couple is sitting next to each other.
There are a total of 16 different ways that they can be seated so the probability of compelement is 16 - 4 = 12, which is 3/4 of the total, meaning that the probability of at least one of the wives sittting next to her husband is 0.75 or 75%.
