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# help with probability

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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 18, 2022

#1
+115
-2

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

sincerely ▄︻デ🇮‌🇫‌1️⃣🇳‌1️⃣🇹‌¥══━一

Apr 18, 2022
#2
+2541
+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 $${8 \over 25} + {3 \over 25} = \color{brown}\boxed{11 \over 25}$$

Apr 18, 2022
#3
+118218
+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

Apr 19, 2022
#4
+9461
+2

Contour map is a nice method! I didn't know it was called "contour map" before.

Here's another probability problem solved with contour maps, which shows the power of contour maps. It makes the problem much more easier.

https://web2.0calc.com/questions/probability_11169#r1

MaxWong  Apr 19, 2022