Question

A carnival game allows the player a choice of simultaneously rolling two, four, six, eight, or ten fair dice. Each die has six faces numbered 1 through 6, respectively. After the player rolls the dice, the numbers that appear on the faces that land up are recorded. The player wins if the greatest number recorded is 1 or 2. How many dice should the player choose to roll to maximize the chance of winning?

Answer 1

Roll two dices

Explanation:

Every dice rolled has two chances of six of winning by showing a 1 or 2, which is the same as one chance of three.

On the opposite, you have four chances of six of loosing by getting a 3,4,5 or 6, which is the same as two chances of three.

Since the chances of loosing are bigger than the ones of winning, every roll makes it more probable of getting a 3,4,5 or 6, so you need to roll as few dices as possible, in this case two is the minimum allowed.