Two Olive Problems - Futility Closet

1. A friend gives you a bottle that contains seven olives. Two of them are green and five are black. He bets that if you remove three olives at random from the bottle, they’ll include a green one. Should you take the bet?

2. Agnes has a tin of olives. It originally contained both black and green ones, but someone has been eating them, so she’s not sure of the colors of the 14 olives that remain. She removes 7 at random and finds that they’re all green. If the odds of this happening were exactly 50-50, what are the colors of the remaining 7?

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1. No: (5/7) × (4/6) × (3/5) = 0.28571428571. The odds are slightly against you even if you draw only two olives. From John Fisher, Never Give a Sucker an Even Break, 1976. 2. One is black and six are green. You can work this out mathematically as above, or make an observation: If there’s a single black olive, it has an equal chance of lying among the first seven olives or the second seven. From Chris Maslanka, “A Bouquet of Brainteasers,” in Barry Cipra’s Tribute to a Mathemagician, 2005.

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