Mathematics

Problem

Two fair dice are thrown simultaneously. Let E

_1

: “the sum of the two numbers is 2, 3 or 4” E

_2

: “the sum of the two numbers is 10, 11 or 12”. a. (i) Show that E

_1

and E

_2

are mutually exclusive. b. (ii) Calculate

P(\text{E}_1)

and

P(\text{E}_2)

. c. (iii) Hence find

P(\text{E}_1\cup\text{E}_2)