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Question
Two different dice are thrown together. Find the probability that the numbers obtained have
1) even sum, and
2) even product.
Solution
Total Number of possible outcomes = 62 = 6*6 = 36 (Two dices are thrown together)
Let A be the event of getting an even sum.
Favourable outcome for event A
= (1,1), (1,3), (1,5),
(2,2), (2,4), (2,6),
(3,1), (3,3), (3,5),
(4,2), (4,4), (4,6),
(5,1), (5,3), (5,5),
(6,2), (6,4), (6,6)
So, there are 18 favourable outcomes. Therefore,
`P(A) = 18/36 = 1/2`
Hence, the probability of getting an even sum is `1/2`
2) Let B be the event of getting an even product
Favourable outcomes for event B
= (1,2), (1,4), (1,6),
(2,1), (2,2),(2,3) (2,4), (2,5), (2,6),
(3,2), (3,4), (3,6),
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),
(5,2), (5,4), (5,6),
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
So, there are 27 favourable outcomes. Therefore,
`P(B) = 27/36 = 3/4`
Hence, the probability of getting an even product is `3/4`
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