@babemomlover,
I don't know how you are supposed to do this formally, and I'm sure there's a shorter way to do it, but that would mean having to learn it instead of just figuring it out. So here's how I'd do it with the caveat that if this is school work I'm sure they are looking for something very different.
babemomlover wrote:Tina randomly selects two distinct numbers from the set {1,2,3,4,5}
Possible combinations:
1+2 = 3
1+3 = 4
1+4 = 5
1+5 = 6
2 +3 = 5
2+4 = 6
2+5 = 7
3+3 = 6
3+4 = 7
3+5 = 8
4+5 = 9
So of those 11 combinations the sums have the following odds:
3 = 1/11
4 = 1/11
5 = 2/11
6 = 3/11
7 = 2/11
8 = 1/11
9 = 1/11
Quote:and Steven randomly selects a number from the set {1,2,3,4,5,6,7,8,9,10}.
10 possibilities.
So there's a 1/11 chance that Tina's sum is 9 and a 1/10 chance that Steven's number is 10.
1/11 x 9/10 = 9/110 so far
There's a 1/11 chance her sum is 8 and a 2/10 chance that Steven's number is greater than 8 so:
1/11 x 8/10 = 8/110 or 17/110 so far.
There is a 2/11 chance her sum is 7, and a 3/10 chance Steven's number is greater so:
2/11 x 7/10 = 14/110 or 31/110 so far
There is a 3/11 chance her sum is 6 and a 4/10 chance Steven's number is greater so:
3/11 x 6/10 = 18/110 or 49/110 so far.
There is a 2/11 chance her sum is 5 and a 5/10 chance Steven's number is greater so:
2/11 x 5/10 = 10/110 or 59/110 so far.
There is a 1/11 chance her sum is 4 and a 6/10 chance Steven's number is greater so:
1/11 x 4/10 = 4/110 or 63/110 so far.
There is a 1/11 chance her sum is 3 and a 7/10 chance Steven's nubmer is greater so:
1/11 x 3/11 = 3/110 or 66/110 (or 40% that his is greater).