Find a probability distribution

Question

A 6 sided and 4 sided die are rolled simultaneously. Let X be the number of twos rolled. Find the probability distribution of X.

Answer 1

X=0,1,2

the 24 outcomes are:

1 1, 1 2 , 1 3 , 1 4

2 1, 2 2 , 2 3 , 2 4

3 1, 3 2, 3 3, 3 4

4 1, 4 2, 4 3 , 4 4

5 1 , 5 2 , 5 3 , 5 4

6 1, 6 2, 6 3, 6 4

Prob(X=0) = 15/24 = 5/8; that is { (1,1), (1,3), (1,4), (3,1), (3,3), (3,4), (4,1), (4,3), (4,4), (5,1), (5,3), (5,4),

(6,1), (6,3), (6,4) }

Prob(X=1) = 8/24 = 1/3 ; that is { (1,2), (2,1), (2,3), (2,4), (3,2), (4,2), (5,2), (6,2) }

Prob(X=2) = 1/24 ; that is (2,2)