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1 . A red box contains the numbers 0, 1, and 2, and a blue box also contains the numbers 0, 1, and 2. You choose a uniformly random element from the red box and a uniformly random element from the blue box; these two choices are independent of each other. Define the random variables

X = the number you choose from the red box,
Y = the number you choose from the blue box,
Z = $\max(X, Y)$.

What is the expected value $\mathbb{E}(Z)$ of the random variable $Z$?

(a)

9/8

(b)

8/9

(c)

9/13

(d)

13/9