Probability

Question

A fair pair of dice is rolled and the sum of the points is noted. What is the probabilit that one of the dice shows 3, given that the sum of the dice is 5. 

Answer 1

P(1st is 3 or 2nd is 3 | sum of 1st and 2nd is 5)

The possibilities of the sum being 5 are:

1 4

4 1

2 3

3 2

 

So there are only 2 possibilities for the above P : 2 3 ; 3 2

 

P(1st is 3 or 2nd is 3 | sum of 1st and 2nd is 5) = 2/4 = 1/2