Math probability

Question

Rework problem 17 from section 3.2 of your text, involving the sum of the numbers showing on two fair dice.

(1) What is the probability that exactly one die shows a 3 given that the sum of the numbers is 4?

Answer 1

2/3 = about 67% it's a 3 if sum = 4

2 ways to get 4, either 3 and 1, or 2 and 2

you might think that means 50% chance it's a 3

but 2 ways to get a 3 with sum = 4, either 3 and 1 or 1 and 3

only 1 way to get 2 and 2

so 2/3 is the probability of a 3 given sum = 4

Pr(sum=2) = 1/36 1+1

Pr(sum=3) = 2/36 1+2 or 2+1

Pr(sum=4) =3/36, 2+2 or 1+3 or 3+1