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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+64 
-3

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

sincerely ▄︻デ🇮‌🇫‌1️⃣🇳‌1️⃣🇹‌¥══━一

 Apr 18, 2022
 #2
avatar+2668 
+1

There are 2 ways to get a positive value: (i) pos×pos or (ii) neg×neg

 

The probability of the second case is: 

 

15×35=325

The probability of the second case is: 

 

25×45=825

 

Thus, the probability is 825+325=1125

 Apr 18, 2022
 #3
avatar+118703 
+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+9675 
+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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