# GMAT Challenge Series (700+): Q8

Question:

Pam and Robin each roll a pair of fair, six-sided dice. What is the probability that Pam and Robin will both roll the same set of two numbers?

A. 1/216

B. 1/36

C. 5/208

D. 11/216

E. 1/18

$$\textit{36 ways that Pam or Robin can roll a pair of fair, six-sided dice}$$  $$\textit{Scenario 1: When the two numbers on the dice are the same}$$ $$\textit{Probabillity of a pair} = \frac{6}{36}$$ $$\textit{Probabillity of the same pair} = \left(\frac{6}{36}\right) \left(\frac{1}{36}\right) = \frac{1}{216}$$  $$\textit{Scenario 2: When the two numbers on the dice are different}$$ $$\textit{Probabillity numbers are different} = \frac{30}{36}$$ $$\textit{Probabillity of the same different numbers} = \left(\frac{30}{36}\right) \left(\frac{2}{36}\right) = \frac{10}{216}$$  $$\textit{Probabillity same set of two nunbers} = \frac{1}{216} + \frac{10}{216} = \frac{11}{216}$$