A = {0, 1, -3, 6, -8} B = {-1, 2, -4, 7} If a is a number t

ardz24 wrote:A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}

If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?

A. 1/4
B. 1/3
C. 2/5
D. 4/9
E. 1/2

I'm confused how to set up the formulas here. Any experts help?

Hi ardz24,
Let's take a look at your question.

A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}
a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, then we will first check for all the possibilities of ab>0 to find the probability.
Total possibilities of making products of two numbers one from set A and other from set B = (Number of elements in Set A) x (Number of elements in set B)
Total outcomes = 5 x 4 = 20

Now, we will find out all the products that are greater than zero i.e. ab>0
1 x 2 = 2
1 x 7 = 7
-3 x -1 = 3
-3 x - 4 = 12
6 x 2 = 12
6 x 7 = 42
-8 x -1 = 8
-8 x -4 = 32
Hence, there are 8 possibilities out of 20 that results into ab>0.
P(ab>0) = 8/20 = 2/5

Therefore, Option C is true.

I am available if you'd like any followup.