Question: 2019 Fall Final - 22

You are given a fair 6-sided red die and a fair 6-sided blue die. Consider the following experiment:

Experiment: Roll each die once and take the sum of the two rolls. You repeat this experiment until the sum of the two rolls is equal to 7. Consider the random variable

• X = the number of times you do the experiment.

(This value $X$ includes the experiment in which the sum is 7 for the first time.)
What is the expected value $\mathbb{E}(X)$ of the random variable $X$?