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Question
Two dice are thrown together. The probability of getting the difference of numbers on their upper faces equals to 3 is ______.
Options
`1/9`
`2/9`
`1/6`
`1/12`
Solution
Two dice are thrown together. The probability of getting the difference of numbers on their upper faces equals to 3 is `underlinebb(1/6)`.
Explanation:
When two dice are thrown,
The sample space (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)}
∴ n(S) = 36
Let A: Event of getting the numbers whose difference is 3.
∴ A = {(1, 4), (2, 5), (3, 6), (4, 1), (5, 2), (6, 3)}
n(A) = 6
∴ Required probability = `(n(A))/(n(S))`
= `6/36`
= `1/6`
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