<s>[INST] Probability of two integers even and greater than seven Found this in a SAT II Math book:
If two integers are selected at random without replacement from the integers 1 through 6 inclusive, what is the probability that the sum of the two integers is even and greater than seven?
I am unsure about how to tackle and "even" and "greater than seven" clauses sine I only know how to use combinations to solve for things like drawing two odd numbers out of the set at the same time or more simple problems of the like. Can someone show me how to solve this problem?
 [/INST] If an odd number is picked, then the second number should also be odd. If an even number is picked, then a second even number should also be picked. Then just do it with brute force.
When 1 is picked, $p=0$.
When 2 is picked, the second number can be 6, $p = \frac{1}{6} \times \frac{1}{5} = \frac{1}{30}$.
When 3 is picked, the second number can be 5, $p = \frac{1}{6} \times \frac{1}{5} = \frac{1}{30}$.
When 4 is picked, the second number can be 6, $p = \frac{1}{6} \times \frac{1}{5} = \frac{1}{30}$.
When 5 is picked, the second number can be 3, $p = \frac{1}{6} \times \frac{1}{5} = \frac{1}{30}$.
When 6 is picked, the second number can be 2,4, $p = \frac{1}{6} \times \frac{2}{5} = \frac{1}{15}$.
Finally, add those possibilities up, $p=\frac{1}{5}$.
Bah, I am really sorry, I made mistake on counting before the edit. Bruce Trumbo is correct.
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