Solution: 2017 Winter Final - 18
Author: Michiel SmidQuestion
You roll a fair red die and a fair blue die, independently of each other. Define the random
variables
- X = "the result of the red die",
- Y = "the result of the blue die",
- Z = $\min(X,Y)$.
(a)
1/6
(b)
5/18
(c)
1/3
(d)
1/4
Solution
Let’s make a table and identify the minimums and when the occur
As we can see, the minimum of 2 occurs 9 times out of the total 36 possibilities
$ Pr(Z=2) = \frac{9}{36} = \frac{1}{4} $