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.
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.
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?