# Math Challenge Problem

The Math Challenge problem has returned to UNC's School of Mathematical Sciences! This is a problem that everyone is welcomed to try their hand at. New problems twice a month.

## November Challenge 2

### Bertrand's Three Coins

Your friend Bertrand has three quarters. One is a regular quarter, but the other two are double sided: one has two heads, the other has two tails. He promises to give you all three coins if you can correctly call a coin he flips. He reaches into his pocket and grabs one of the quarters at random, and without looking, flips it into the air. You call "tails." It lands heads.

Feeling sorry for you, he offers you another chance. You can choose to flip the coin over and reveal the other side, or he can flip one of the remaining coins (chosen at random) and see how it lands. You win if the result of your choice is tails. Which is the better choice?

The Challenge: Which is more likely: that the other side of the first coin is a tails, or that a randomly chosen coin from the remaining two will flip to tails? And why are they not equally likely?

Submit solutions to Ross 2239G or by email to oscar.levin@unco.edu.

Win PRIZES! A winner will be selected from all correct answers received for each challenge problem to receive a fun math prize of his or her choice.

## Previous Problems

### Contact Information

• School of Mathematical Sciences, University of Northern Colorado
• Ross 2239
• Campus Box 122
• 501 20th Street
• Greeley, CO 80639
• Tel: (970) 351-2820
• Fax: (970) 351-1225