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 January 20th, 2019, 05:52 PM #1 Senior Member   Joined: Dec 2015 From: iPhone Posts: 486 Thanks: 75 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: 772 Thanks: 279 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: iPhone Posts: 486 Thanks: 75 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
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Quote:
 Originally Posted by idontknow I know, but is there a method?
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: 2,408 Thanks: 1309 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
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Quote:
 Originally Posted by idontknow I know, but is there a method?
Using what you know, did you get an answer? If so, can you post that answer, including the assumptions you made and all of your working?

 January 21st, 2019, 12:18 PM #7 Senior Member   Joined: Dec 2015 From: iPhone Posts: 486 Thanks: 75 $\displaystyle P(xy\leq 24)=1-P(xy=25)=1-\frac{1}{9}=\frac{8}{9}$ .
 January 21st, 2019, 12:32 PM #8 Global Moderator   Joined: Dec 2006 Posts: 20,484 Thanks: 2041 If you want to generalize that method, what aspect of the problem is to be generalized?
January 21st, 2019, 01:51 PM   #9
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Quote:
 Originally Posted by romsek 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.
Ignore this. I didn't see all of the problem.

 January 21st, 2019, 02:34 PM #10 Senior Member   Joined: Dec 2015 From: iPhone Posts: 486 Thanks: 75 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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