if a pair of fair dice is rolled, what is the probability that we roll a total of five if we are given that the total is less than nine?

Answer 1

total less than nine
lets look at the ways to get nine or more
4,5; 4,6 four ways to do that
5,5; 5,6 four ways to do that
6,6 one way to do that.

Now, ways to get less than 9=
ways to throw two die, minus way to get nine or more= 36-9above=29 ways check that.
Now, if we roll a five, we have to
4,1 two ways to do that
3,2 two ways to do that.

Pr(5, given nine or less)=4/29

check all this, I have been up all night.

Answer 2

4/30