# Problem 8

# Dice sum collisions

**Due**: January 19

**Points**: 1

In class, we saw that the probability of rolling two 6-sided dice and getting the same number on each one is \(\tfrac{1}{6}\).

Now suppose you roll 2 dice at a time, and add up the two numbers. What is the probability of doing this twice and getting the same sum both times? That is, if you roll 4 dice total, then add up the numbers on the first two dice and the numbers on the last 2 dice, what is the chance that these two sums are the same?

(Hint: Look at the top half of page 5 and the bottom half of page 11 in the book chapter by Jean Gallier listed at the beginning of the Unit 1 notes page.)