if two fair dice are rolled, find the probability that the sum of the dice is 8, given the sum is greater than 7

Answer 1

two dice have 11 possible outcomes from 2 to 12

P(2) = 1/36 = P(12)

P(3) = 2/36 = P(11)

P(4) = 3/36 = P(10)

P(5) = 4/36 = P(9)

P(6) = 5/36= P(8)

P(7) = 6/36

P(8) = 5/36

P(>7) =15/36 = 5/12

add up P(8)+P(9)+P(10) + P(11) +P(12 = (5+4+3+2+1)/36 = 15/36 = 5/12

7 is the most likely with P(7) = 1/6

P(>7)= P(<7) = (1-1/6)/2 = (5/6)/2 = 5/12