
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
January 20th, 2019, 05:52 PM  #1 
Senior Member Joined: Dec 2015 From: somewhere Posts: 634 Thanks: 91  Need explanation on probability
$\displaystyle x+y=10 \; \; $ , x and y are natural numbers. Find probability such that $\displaystyle xy\leq 24$ . 
January 20th, 2019, 05:57 PM  #2 
Senior Member Joined: Oct 2009 Posts: 863 Thanks: 328 
You can easily do this by brute force. Start by listing all natural number pairs (x,y) for which x+y=10. Then what proportion has the condition you specified?

January 20th, 2019, 05:59 PM  #3 
Senior Member Joined: Dec 2015 From: somewhere Posts: 634 Thanks: 91 
I know, but is there a method?
Last edited by skipjack; January 21st, 2019 at 01:49 AM. 
January 20th, 2019, 06:46 PM  #4 
Senior Member Joined: Oct 2009 Posts: 863 Thanks: 328  Yes. I gave you one in my post.
Last edited by skipjack; January 21st, 2019 at 01:50 AM. 
January 20th, 2019, 07:09 PM  #5 
Senior Member Joined: Sep 2015 From: USA Posts: 2,549 Thanks: 1399 
It should be pretty obvious that there are a finite number of natural number pairs that sum to 10. At the same time it's clear that set of all natural number pairs is infinite in extent. Thus the probability of a pair of natural numbers summing to 10 is zero. 
January 21st, 2019, 01:49 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,968 Thanks: 2216  
January 21st, 2019, 12:18 PM  #7 
Senior Member Joined: Dec 2015 From: somewhere Posts: 634 Thanks: 91 
$\displaystyle P(xy\leq 24)=1P(xy=25)=1\frac{1}{9}=\frac{8}{9}$ .

January 21st, 2019, 12:32 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,968 Thanks: 2216 
If you want to generalize that method, what aspect of the problem is to be generalized?

January 21st, 2019, 01:51 PM  #9 
Senior Member Joined: Sep 2015 From: USA Posts: 2,549 Thanks: 1399  Ignore this. I didn't see all of the problem.

January 21st, 2019, 02:34 PM  #10 
Senior Member Joined: Dec 2015 From: somewhere Posts: 634 Thanks: 91 
First of all the problem is unuseful and rare, just posted it to see what is available. To solve it the steps are below: (1) Find number of pairs (x,y) such that x+y=10 . (2) Find the range of xy with constraint x+y=10 . 

Tags 
explanation, probability 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Question re probability of explanation of Exam procedure  Stuart B W  Advanced Statistics  1  July 10th, 2015 03:43 AM 
Explanation Required with Probability Question(s)  MathGuruInTraining  Probability and Statistics  0  July 9th, 2014 02:34 PM 
Probability (explanation needed)  Nerazzurri_KZ  Probability and Statistics  5  April 3rd, 2011 04:36 AM 
probability (explanation is needed)  safyras  Probability and Statistics  1  April 2nd, 2011 07:29 PM 
probability (explanation is needed)  safyras  Probability and Statistics  1  March 31st, 2011 02:23 PM 