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 ______.

पर्याय

• `1/9`

• `4/9`

• `1/18`

• `1/2`

Answer 1

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`