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January 20th, 2019, 06:52 PM  #1 
Senior Member Joined: Dec 2015 From: iPhone Posts: 380 Thanks: 60  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, 06:57 PM  #2 
Senior Member Joined: Oct 2009 Posts: 732 Thanks: 249 
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, 06:59 PM  #3 
Senior Member Joined: Dec 2015 From: iPhone Posts: 380 Thanks: 60 
I know, but is there a method?
Last edited by skipjack; January 21st, 2019 at 02:49 AM. 
January 20th, 2019, 07:46 PM  #4 
Senior Member Joined: Oct 2009 Posts: 732 Thanks: 249  Yes. I gave you one in my post.
Last edited by skipjack; January 21st, 2019 at 02:50 AM. 
January 20th, 2019, 08:09 PM  #5 
Senior Member Joined: Sep 2015 From: USA Posts: 2,299 Thanks: 1222 
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, 02:49 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,262 Thanks: 1958  
January 21st, 2019, 01:18 PM  #7 
Senior Member Joined: Dec 2015 From: iPhone Posts: 380 Thanks: 60 
$\displaystyle P(xy\leq 24)=1P(xy=25)=1\frac{1}{9}=\frac{8}{9}$ .

January 21st, 2019, 01:32 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,262 Thanks: 1958 
If you want to generalize that method, what aspect of the problem is to be generalized?

January 21st, 2019, 02:51 PM  #9 
Senior Member Joined: Sep 2015 From: USA Posts: 2,299 Thanks: 1222  Ignore this. I didn't see all of the problem.

January 21st, 2019, 03:34 PM  #10 
Senior Member Joined: Dec 2015 From: iPhone Posts: 380 Thanks: 60 
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 . 

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