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Answer:
Step-by-step explanation:
The sample space of rolling a dice twice is:
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)}
Sample size, <em>n</em> = 36.
Each sample has an equal chance of being selected.
So the probability of selecting any of the 36 sample is, .
Now an event <em>A</em> is defined as the second roll being larger than the first.
The sample space for <em>A</em> is:
<em>A</em> = {(2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (5, 3), (5, 4), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5)}
The sample size is, <em>n</em> = 15.
The probability of the event <em>A</em> is: