Monty, Monty, Monty

I'm reading The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow (Linkcat: The Drunkard's walk : how randomness rules our lives)

Here are a couple of nice problems:


A woman is going to have two children. Given that one of them will be a girl, what are the odds that BOTH will be girls?



You are on Monty Hall. There are three doors on the floor. Behind one door is a new IPOD Touch, behind each of the other two doors are goats. You pick door #1. Monty, who knows what is behind all the doors, opens door #2 to reveal a goat. He asks if you want to stick with door #1 or change to door #3. Should you change or not?

Answers below if you scroll down:



















The odd of both being girls given that one is a girl is NOT 50%, but rather 1 in 3.



Yes, you should change doors. The host's actions skew the odds in favor of changing.

The Let's Make a Deal Applet - Give it a try.

http://montyhallproblem.com/

Monty Hall Dilemma from Interactive Mathematics Miscellany and Puzzles