The role of probability in solving the Monty Hall problem

[Jenny A]

Use three shoe boxes. Put a dollar in one and a penny in another and a nickel in the third. The dollar is the grand prize the coins, duds. Close the lids.

Presuming the contestant switches here are the three equal possibilites.

1. He chooses the box with the penny. You peek in the other two boxes and open the one with the nickle. He switches to the box you did not reveal and gets the dollar.
2. He chooses the box with the nickle. Your peek in the other two boxes and reveal the penny.. He switches to the box you did not reveal and gets the dollar.
3. He chooses the box with the dollar. You peek in the other two boxes and reveal either the penny or the nickle. Whichever you reveal he switches and gets the other coin. He loses.

Notice that by switching he gets the dollar two out of three choices.

Suppose he doesn't switch. Your actions remain the same, but he only gets the dollar if he chooses it to begin with. So if he doesn't switch he has only has a one in three chance of winning.