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Given that a and b are real numbers such that -3 ≤ a ≤ 2 and -1 ≤ b ≤ 4, and values for a and b are chosen at random, what is the probability that product a*b is positive?

 Apr 29, 2022
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Translate  -3 <= a <= 2  into   -3 <= x <= 2  and  -1 <= b <= 4  into  -1 <= y <= 4 

and place this region onto a regular  x-y  plane.

 

The total region covered is  5 · 5  =  25  square units.

 

The positive product region is  (2 · 4) +  (-3 · -1)  =  8 + 3  =  11  square units.

 

The probability of landing on the positive region is  11 / 25.

 Apr 29, 2022

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