The probability that at least one number is odd and the sum of the two numbers is even is 1/4
The probability that exactly one number is 6 and the product of the two numbers is at most 15 is 1/9
The easiest way to figure out probability problems with small data sets is to write out your entire sample space and then divide by the total:
Sample size = 6 * 6 = 36
S = {[1,1],[1,2],[1,3],[1,4],[1,5],[1,6],[2,1],[2,2],[2,3],[2,4],[2,5],[2,6],[3,1],[3,2],[3,3],[3,4],[3,5],[3,6],[4,1],[4,2],[4,3],[4,4],[4,5],[4,6],[5,1],[5,2],[5,3],[5,4],[5,5],[5,6],[6,1],[6,2],[6,3],[6,4],[6,5],[6,6]}
The only way to make a number combination that's even while 1 die is odd is to have 2 odd numbers.
{[1,1],[1,3],[1,5],[3,1],[3,3],[3,5],[5,1],[5,3],[5,5]}
This gives us 9 results.
The probability of this happening is 9/36 = 1/4 = 0.25
Now if we have to get a 6 with the product being at most 15 we know that the biggest number that 6 can be multiplied by is 2 which gives us 12.
We are left with 4 options:
{[1,6],[2,6],[6,1],[6,2]}
The probability of this happening is 4/36 = 1/9 = 0.1111...
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