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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
avatar+122 
-2

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

sincerely ▄︻デ🇮‌🇫‌1️⃣🇳‌1️⃣🇹‌¥══━一

 Apr 18, 2022
 #2
avatar+1384 
+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
avatar+117236 
+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
avatar+9369 
+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

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