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# help

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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.

Logic  Nov 25, 2018
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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

CPhill  Nov 25, 2018