A pair of fair 6sided dice is rolled What is the probability

A pair of fair 6-sided dice is rolled. What is the probability that a 3 is rolled if it is known that the sum of the numbers landing uppermost is less than or equal to 6?

Solution

you can roll a 1,2, 4, 5, or 6

1,1
1,2

1,3

1,4

1,5

2,1

2,2

2,3

2,4

3,1
3,2

3,3

4,1

4,2

5,1

TOTAL OUTCOME WITH LESS THEN 6 ARE 15 BUT WITH ATLEAST ONE 3 THERE ARE 5

SO THE PROBABILITY = 5/15 = 1/3