The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

   

Sally's Bets

Recently you invited your friend Sally- a mathematician by vocation and gambler by vice - to a dinner party with some married couples. You knew the couples only a little, and you were quite sure Sally knew them not at all. In a demonstration of the subtleties of probability, she offered a series of three wagers.

She turned to the couple immediately to her left and inquired how many children they had. "Two," they replied.

"And is the oldest a girl?" she asked.

"Yes."

Turning to you she offered, "I'll wager even money that the other child is a boy."

Next, Sally turned to the couple on her right and asked the same question about their progeny. Again, "two" was the answer.

"And, of your children, is one of them a girl?" she asked.

"Yes."

Turning to you she said, "I'll wager even money that the other child is a boy."

"Finally, I'll let you know that I have exactly one sibling, and that sibling is younger than I. Will you wager even money that the sibling is a boy?"

Sally was trying to prove a point about the subtleties of probability - she knew nothing about the children of the couples present. What were your odds of collecting on each of three wagers?


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