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?
+64 Nice example here https://web2.0calc.com/questions/help_20481
sincerely ▄︻デ🇮🇫1️⃣🇳1️⃣🇹¥══━一
+2668 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 \({8 \over 25} + {3 \over 25} = \color{brown}\boxed{11 \over 25} \)
+118659 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
