Question

A die is thrown twice. What is the probability that

1. 5 will not come up either time?
2. 5 will come up at least once?

[Hint: Throwinga die twice and throwing two dice simultaneously are treated as the same experiment].

Answer 1

All possible outcomes are:

(1, 1); (1, 2); (1, 3); (1, 4); (1, 5); (1, 6).

(2, 1); (2, 2); (2, 3); (2, 4); (2, 5); (2, 6).

(3, 1); (3, 2); (3, 3); (3, 4); (3, 5); (3, 6).

(4, 1); (4, 2); (4, 3); (4, 4); (4, 5); (4, 6).

(5, 1) ; (5, 2); (5, 3); (5, 4); (5, 5); (5, 6).

(6, 1) ; (6, 2); (6, 3); (6, 4); (6, 5); (6, 6).

All possible outcomes = 36

(i) Let E be the Event that 5 does not come up either time

Number of favourable Outcomes = 36 − (5 + 6) = 25

∴ p (E) = `25/36`

(ii) Let N be the event that 5 will come up at least once, then number of favourable outcomes = 5 + 6 = 11

∴ P (N) = `11/36`