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Question
A pair of dice is rolled. If the outcome is a doublet, a coin is tossed. Determine the total number of elementary events associated to this experiment.
Solution
If a pair of dices is thrown simultaneously, then all possible outcomes = 6 × 6 = 36
The set of these outcomes is the sample space, which is given by
S = { (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)}
Again, if the outcome is a doublet, then a coin is tossed.
Now, we have the following events:
{(1, 1, H), (2, 2, H), (3, 3, H), (4, 4, H), (5, 5, H), (6, 6, H),
(1, 1, T), (2, 2, T), (3, 3, T), (4, 4, T), (5, 5, T), (6, 6, T)}
Total number of events when the outcome is a doublet = 6 x 2 = 12
Hence, the total number of elementary events associated with this experiment = (36 − 6) + 12 = 42
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