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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?

 Feb 3, 2019
 #1
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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

 

 

cool cool cool

 Feb 3, 2019

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