If two fair dice are​ rolled, find the probability that the sum of the dice is 8​, given that the sum is greater than 4.

Answer 1

(1,1)(2,1)(3,1)(4,1)(5,1)(6,1)

(1,2)(2,2)(3,2)(4,2)(5,2)(6,2)

(1,3)(2,3)(3,3)(4,3)(5,3)(6,3)

(1,4)(2,4)(3,4)(4,4)(5,4)(6,4)

(1,5)(2,5)(3,5)(4,5)(5,5)(6,5)

(1,6)(2,6)(3,6)(4,6)(5,6)(6,6)

By conditional probability, we can count the number of sums that is greater than 4. This gives us 31. Out of 31, 5 are equal to the sum of 8.

P(Sum is 8 | Sum greater than 4) = 5/31