From a first glence, I'd pick C

Analyzing the problem:

Set: [-5, -4, -3, -2, -1, 0, 1, 2, 3] (total 9 integers)

# negatives: 5

# positives: 3

# Zeros: 1

# Evens: 4

# Odds: 5

Now, lets calculate the probablity or the likelyhood of each event:

(A) The sum of the two integers is even
That'll be when picking 2 odds or 2 evens

P(A)= 5/9 x 4/8 + 4/9 x 3/8 = 32/72 = 4/9

(B) The sum of the two integers is odd
That holds when picking 1 odd and 1 even

P(B) = 5/9 x 4/8 + 4/9 x 5/8 = 2 x 20/72 = 40/72 = 5/9

(C) The product of the two integers is even
That'll be true when picking eithe 1 even 1 odd or 2 evens.

P(C) = P(B) + 4/9 x 3/8 = 5/9 + 12/72 = 5/9 + 1/6 = 39/54

(D) The product of the two integers is odd
That holds when picking two odds only ..

P(D) = 5/9 x 4/8 = 20/72 = 5/18 = 2.5/9

(E) The product of the two integers is negative
that holds when picking one negative and one positive

P(E) = 5/9 x 3/8 + 3/9 x 5/8 = 30/72 = 5/12

Yahoooo. My first glence worked out perfectly and my stats courses in college are helping me now

..

39/54 has the largest value among all answer choices.

Answer: C