Question

There are six chairs in a row. Person A picks one of the chairs at random. Then Person B picks a chair at random from the five chairs that remain. Find the chance that they pick chairs that are next to each other

Answer 1

Person A has a 1/3 chance of picking a chair on the end, for which Person B has a 1/5 chance of picking the adjacent chair. Probability of this event is pA * pB = 1/15. In the remaining scenarios, Person B has a 2/5 chance of picking an adjacent chair while Person A has a 2/3 chance of picking a non-end chair. Probability of the second event occuring is pA * pB = 4/15. Since both scenarios are mutually exclusive, the probability of either occuring is the sum of the two probabilities; pS1 + pS2 = 5/15 = 1/3.

I'm actually riffing on this. The result seems higher than intuitively perceived.

Answer 2

1/3