A pair of dice is constructed so that each die is marked with a 1 on one side a 2 on two sides and a 3 on three sides The dice are rolled Find the probability that the same number appears on each?

Let X be the number that is rolled

P(X=1) = 1/6

P(X=2) = 2/6

P(X=3) = 3/6

Case 1 (2 ones are rolled)

(P(X=1))(P(X=1)) = 1/36

Case 2 (2 twos are rolled)

(P(X=2))(P(X=2)) = 4/36

Case 3 (2 threes are rolled)

(P(X=3))(P(X=3)) = 9/36

Probability of same number appearing on each =

(Case 1)U(Case 2)U(Case 3) since they are independent this equals

Case1 + Case2 +Case3=

1/36 +4/36 + 9/36 = 14/36