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Question
If the sum of numbers obtained on throwing a pair of dice is 9, then the probability that number obtained on one of the dice is 4, is ______.
Options
`1/9`
`4/9`
`1/18`
`1/2`
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Solution
If the sum of numbers obtained on throwing a pair of dice is 9, then the probability that number obtained on one of the dice is 4, is `underlinebb(1/2)`.
Explanation:
When two dice are thrown, then
Total probable cases, n(S) = 36
Cases when the sum of 9 is obtained,
A = (3, 6), (6, 3), (4, 5), (5, 4)
n(A) = 4
∴ P(A) = `4/36 = 1/9`
Now, cases when there is 4 on one of dice (sum is 9).
B = (4, 5), (5, 4),
∴ n(A ∩ B) = 2
P(A ∩ B) = `2/36`
Required probability
`P(B/A) = (P(B ∩ A))/(P(A))`
= `(2/36)/(4/36)`
= `1/2`
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