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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?

Guest Feb 3, 2019

#1**+1 **

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

CPhill Feb 3, 2019