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avatar+1196 

Given that \(a\) and \(b\) are real numbers such that \(-3\leq a\leq1\) and \(-2\leq b\leq 4\), and values for \(a\) and \(b\) are chosen at random, what is the probability that the product \(a * b\) is positive? Express your answer as a common fraction.

 Nov 25, 2018
 #1
avatar+107348 
+1

I'm using   x for a and y for b

 

Look at the graph, here :  https://www.desmos.com/calculator/5iayh796gi

 

The  region formed by the first two inequalities is 24 units^2

 

The region formed by ab > 0 ⇒ xy > 0    is split into two rectangles

One is 3 x 2   = 6 units^2

And the other is 1 x 4 = 4 units^2

 

So....the probability that   ab > 0   ⇒  xy > 0  is  

 

[ 6 + 4 ] / 24    =  10 / 24    =    5 / 12

 

 

cool cool cool

 Nov 25, 2018

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