A pair of dice is rolled. Find the probabilities of the given events.

Question

A pair of dice is rolled. Find the probabilities of the given events.

(a) The sum is 4.

 I know this is 1/12

(b) The sum is 4, given that the sum is less than 6.

(c) The sum is less than 6, given that the sum is 4.

I can not figure out part b and c, any help is greatly appreciated

Answer 1

b.

How many of the 36 possible combinations are less than 6:

1 and 4

4 and 1

2 and 3

3 and 2

1 and 3

3 and 1

2 and 2

2 and 1

1 and 2

1 and 1

there are 10

out of those 10, how many sum to 4 - there are 3: 1 and 3, 3 and 1, 2 and 2

so probability is 3/10

c.

if the sum is 4 then it has to be less than 6 all the same - so probability is 1