Question

Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.

Answer 1

When two dice are thrown, the sample space S has 6 × 6 = 36 sample points. 

∴ n(S) = 36 

Let X denote the number of sixes when two dice are thrown. 

Then X can take values 0, 1, 2 

When X = 0, then 

X = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5)} 

∴ n(X) = 25

When X = 1, then 

X = {(1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5)} 

∴ n(X) = 10

When X = 2, then X = {(6, 6)}