A gambler rolls three fair six-sided dice. What is the probability

This is a tricky question because there is a final twist that it is easy to overlook.

First off, we want to find the probability of rolling a pair of any number. There are six
pairs and a total of 36 different ways to roll a pair of dices: 6/36 = 1/6.

Next, we want to account for the third die - it cannot be the same as the first two,
so it can be any of five numbers out of 6: 5/6.

Therefore probability is 5/6 x 1/6 = 5/36.

It is tempting here to think that we have solved the problem. But if we read carefully, the
question does not say that the first two dice have to be the same and the third die has
to be different.

the question says a gambler rolls 3 dice. So the first two do not have to be pairs.
As long as 2 of the 3 dice are pairs and the last die is a different number. To find the
number of way this can occur, we use combinations formula: 3!/2!1! = 3.

We multiply this to the numerator to give us 3 x 5/36 = 15/36.

For some even trickier dice problems, check out our Magoosh GMAT blog post (these ones are really nasty!)

GMAT Probability: Difficult Dice Questions