Two fair dice are thrown once.

MATHEMATICS · Multi-part · AP · AP Statistics · Probability Random Variables Distributions · Probability Random Variables Distributions

Problem

Two fair dice are thrown once. (i) Let

A =

“the sum of the numbers on the two dice is even” and

B =

“the sum is odd”. Show that

A

and

B

are mutually exclusive and exhaustive. (ii) Using the result of part (i), state whether

A

and

B

are complementary, giving a brief reason. (iii) Calculate

P(A)

P(B)

and

P(A\cup B)