Given that a and b are real numbers such that -3 ≤ a ≤ 1 and -2 ≤ b ≤ 4, and values for a and b are chosen at random, what is the probability that the product a*b is positive?
+128407 Let's use "x" for "a" and "y" for b
We can solve this with a graph
The region created by the inequalities will be a 4 x 6 rectangle = 24 units^2
But the only values of (x, y) that produces a positive product for xy will be where x and y have the same signs
These areas will consist of a 3 x 2 rectangle and a 4 x 1 rectangle
So...the total of these areas is 6 + 4 = 10
So....the probability that xy = ab is positive is 10 /24 = 5 /12
Here's a graph to give you a feel for this :
https://www.desmos.com/calculator/834uyfbxoo
