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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, wha

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Given that  and  are real numbers such that  and , and values for  and  are chosen at random, what is the probability that the product  is positive? Express your answer as a common fraction.

Aug 11, 2021

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Hi Guest,

I will try to solve this.

{CORRECTION}: I did not read that it wanted product

A is between -3, and 1

So the possibilities are -3, -2, -1, 0, 1

B is between -2 and 4

So the possibilities are -2, -1, 0, 1, 2, 3, 4

Not counting zero, A has 3 negative, B has 2 negative

Not counting zero, A has 2 positive, B has 4 positive

A and B must both be negative, or positive

A negative possibiliteis * B negative possibilities = 3/4 * 2/6 = 6/24 = 1/4

A positive possibilities * B positive possibilities = 1/4 * 4/6 = 4/24 = 1/6

1/4 + 1/6 = 3/12 + 2/12 = 5/12

Aug 11, 2021
edited by Bulbous  Aug 11, 2021