Carcass wrote:
What is the probability of choosing 2 distinct positive integers from the set of first 10 positive integers such that their product and sum are both even?
A. 1/5
B. 2/9
C. 2/5
D. 4/9
E. 1/2
If two integers have an even product AND an even sum, then
the two integers must both be evenSo, the question is really asking us to find
P(the 2 selected integers are both even). The set of first 10 positive integers consists of 5 odd integers and 5 even integers.
So, we get:
P(the 2 selected integers are both even) = P(the 1st integer is even
AND the 2nd integer is even)
= P(the 1st integer is even)
x P(the 2nd integer is even)
= 5/10
x 4/9
= 2/9
Answer: B