Amy and Becky are two friends invited to a 5-member committee meeting. What is the probability that they get seats next to each other if:
1. the member seats are arranged in a round table
2. the member seats are arranged in a row
Seated around a roundtable
Given that Amy is seated as denoted in the figure, Becky can sit next to her if she gets one of the two seats marked as Betty. In a random seating assignment case, the probability for that to happen is 2 out of 4 or the probability for the two seated side by side is 2/4 = 50%
Seated in a row
As we did before, let’s place Amy first.
In the end – two such places (E)
In the middle – three such places (M)
Only one person can be next to the position E’s, but two positions are possible for M’s. A series of AND and OR rules estimate the overall possibility.
(Amy on E1 OR E2) AND (Becky on position 1) OR (Amy of M2 OR M3 OR M4) AND (Becky on position 1 OR Position 2).
(1/5+1/5) x (1/4) + (1/5+1/5+1/5) x (1/4 + 1/4)
2/20 + 6/20 = 8/20 = 40%
Reference
How To Solve Bloomberg’s Random Seating Interview Question: MindYourDecisions
