It’s a Puzzlement
By Walter Wright
Sometimes, when reviewing past issues of The Actuarial Review to find items that would be interesting for this column, the pickings are slim. But the puzzle column invariably is a good candidate, offering timeless puzzles that are still challenging. Here’s Charlie Hewitt’s contribution to Wayne H. Fisher’s column from 25 years ago. (Note: Although I solved it, I couldn’t do so within Charlie’s suggested time frame. Maybe I could have 25 years ago. Maybe you can today.)
This issue’s puzzlement is a quickie submitted by Charlie Hewitt. If this were Part 2, you’d have to complete it in under 5 minutes. Any takers?
Reggie Bayes, a rabid sports fan, has to leave the United States on the first day of a championship series. About to board a plane for an actuarial assignment in Bora Bora, Reggie learns that Team A has just won the first game of the “best four-out-of-seven” event.
Upon arrival in Bora Bora, Reggie is disheartened to find that there is no source of U.S. sports news. However, on the last day of Reggie’s assignment a “ham” radio operator picks up a garbled announcement to the effect that the series ended with the sixth game; unfortunately, the name of the winning team is lost in the transmission.
If Reggie calculates that Team A and Team B were equally likely to win in a six-game series (given that Team A won the first game), what relative probabilities does Reggie assign to Team A and Team B for winning any one game? Express your answer analytically, i.e., not as a decimal.