Question

A die is rolled twice. What is the probability that the sum of the faces is greater than 7, given that

(a) 2 appears on one side of the rolls

(b) first outcome was 4

(c) first outcome greater than 3

Answer 1

there is a total of 6*6 =36 combinations

a) total number of ways to form a sum greater than 7 given 2 appears on one side of the roll is 2

(2,6) (6,2)

Hence the required probability is

b) the total number of ways to form a sum greater than 7 given 4 appears on first is 3

(4,4) (4,5) (4,6)

Hence the required probability is

c)

the total number of ways to form a sum greater than 7 given the first outcome is greater than 3 is 12

(4,4) (4,5) (4,6)

(5,3) (5,4) (5,5) (5,6)

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

Hence the required probability is