# TV Show

You are in a TV show where in the final round the host gives you the option to open one of three boxes and to receive the reward inside. Two of the boxes contain just a penny, while the third box contains \$1.000.000. In order to make the game more exciting, after you pick your choice, the rules require the host to open one of the two remaining boxes, such that it contains a penny inside. After that he asks you whether you want to keep your chosen box or to switch it with the third remaining one. What should you do?

## SOLUTION

This is the so called "Monty Hall" problem. The answer is that in order to maximize your chances of winning \$1.000.000, you should switch your box. The reason is that if initially you picked a box with a penny, then after switching you will get a box with \$1.000.000. If initially you picked a box with \$1.000.000, then after switching you will get a box with a penny. Since in the beginning the chance to get a penny is 2/3, then after switching your chance to get \$1.000.000 is also 2/3. If you stay with your current box, then your chance to get \$1.000.000 will be just 1/3.