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?

Guest Apr 18, 2022

#1**-2 **

Nice example here https://web2.0calc.com/questions/help_20481

sincerely ▄︻デ🇮🇫1️⃣🇳1️⃣🇹¥══━一

Kakashi Apr 18, 2022

#2**+1 **

There are 2 ways to get a positive value: (i) \(\text{pos} \times \text{pos}\) or (ii) \(\text{neg} \times \text{neg}\)

The probability of the second case is:

\({1 \over 5} \times { 3 \over 5} = {3 \over 25}\)

The probability of the second case is:

\({2 \over 5} \times { 4 \over 5} = {8 \over 25}\)

Thus, the probability is \({8 \over 25} + {3 \over 25} = \color{brown}\boxed{11 \over 25} \)

BuilderBoi Apr 18, 2022

#3**+3 **

Thanks BuilderBoi, you are correct of course.

I just wanted to show people how to do it with a contour map.

I really like contour maps, in this case it was probably as easy either way but sometimes contour maps make probablility questions MUCH easier.

The sample space is 5*5 = 25 (area)

The desirable area is 2*4+ 1*3 = 8+3 = 11

So P(positive product) = 11/25

Melody Apr 19, 2022