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Question
A die is thrown twice. What is the probability that
- 5 will not come up either time?
- 5 will come up at least once?
[Hint: Throwinga die twice and throwing two dice simultaneously are treated as the same experiment].
Solution
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`
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