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January 20th, 2019, 06:52 PM   #1
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Need explanation on probability

$\displaystyle x+y=10 \; \; $ , x and y are natural numbers.
Find probability such that $\displaystyle xy\leq 24$ .
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January 20th, 2019, 06:57 PM   #2
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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?
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January 20th, 2019, 06:59 PM   #3
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I know, but is there a method?

Last edited by skipjack; January 21st, 2019 at 02:49 AM.
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January 20th, 2019, 07:46 PM   #4
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Quote:
Originally Posted by idontknow View Post
I know, but is there a method?
Yes. I gave you one in my post.

Last edited by skipjack; January 21st, 2019 at 02:50 AM.
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January 20th, 2019, 08:09 PM   #5
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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.
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January 21st, 2019, 02:49 AM   #6
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Quote:
Originally Posted by idontknow View Post
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?
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January 21st, 2019, 01:18 PM   #7
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$\displaystyle P(xy\leq 24)=1-P(xy=25)=1-\frac{1}{9}=\frac{8}{9}$ .
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January 21st, 2019, 01:32 PM   #8
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If you want to generalize that method, what aspect of the problem is to be generalized?
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January 21st, 2019, 02:51 PM   #9
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Quote:
Originally Posted by romsek View Post
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.
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January 21st, 2019, 03:34 PM   #10
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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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