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#1 2006-01-20 13:13:16

Draven
Guest

Calculating Odds

Hello, I would like to know the odds of getting the total of 3 RANDOM 3 digit numbers correct without ever seeing the numbers.

For example:

345
231
142+
------

I would NOT ever see these numbers and I would take a guess at the total such as 1568, what would be the odds of my total being correct? Thanks!

#2 2006-01-20 13:45:16

Ricky
Moderator

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Re: Calculating Odds

Depends how you define a 3 digit number.  Is 001 a three digit number?

Assuming that it isn't, 100 is the smallest three digit number.  100 + 100 + 100 = 300 is the smallest sum of three digit numbers.  999 + 999 + 999 = 2997.  All other numbers inbetween these two are also valid.  That is, the range of answers is [300, 2997].  This means the number of possible answers is 2997 - 300 = 2697.  When you take 1 guess, you have a 1/2697 chance of getting it right.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

#3 2006-01-20 15:02:02

Draven
Guest

Re: Calculating Odds

I am a performer (Mind Reader) and I needed to know for one of my effects and I'm not very good with math. Thanks very much!

#4 2006-01-20 22:31:34

mathsyperson
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Re: Calculating Odds

Technically, the probability would change depending on which total you chose.

For example, the number 300 could only be made from (100, 100, 100), but 700 could be made from (500, 100, 100), (499, 101, 100) and many, many others.

The total number of combinations is 729000000 and each number between 300 and 1649 would have a different probability, after that the probabilities would mirror the probabilities that have already been.

But if you're just using the statistic as a small part of your act, like "There is a 1 in 2697 chance that I will get this right!", then the 1/2697 thing will do fine. Just don't complain to us if someone in the audience points out what I've just said. wink


Why did the vector cross the road?
It wanted to be normal.

#5 2006-01-22 15:34:26

Draven
Guest

Re: Calculating Odds

Well it doesn't matter too much, but if it's easy for you guys to give me the answer than the odds for the total of "1455" would be helpful. If it's difficult though it's not that important. Thanks!smile

#6 2006-01-24 02:24:47

mathsyperson
Moderator

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Re: Calculating Odds

Thanks to the power of Excel, I can now reveal that the probability is 570058/729000000.

Roughly speaking, that's around 1 in 1300.


Why did the vector cross the road?
It wanted to be normal.

#7 2006-01-24 04:39:55

Ricky
Moderator

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Re: Calculating Odds

You used excel to find the number of permutations for each sum, from 300 to 2997?  How, and how long did that take?

And is it permutations or combinations?  Order doesn't matter, does it?


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

#8 2006-01-24 04:59:18

mathsyperson
Moderator

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Re: Calculating Odds

The spreadsheet works out permutations, which is what's needed here.

And it didn't take too long. I worked out the number of ways it could be the numbers from 100-999 with one random number (1 each), then worked out the number of ways it could be 200-1998 with two (1, 2, 3, 4, ... 900, 899, 898, ..., 1), then used various summations of those values to work out the final values. There's probably a faster way of doing it, but this way's quite simple. n_n


Why did the vector cross the road?
It wanted to be normal.

#9 2006-01-24 09:02:34

MathsIsFun
Administrator

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Re: Calculating Odds

mathsyperson wrote:

Technically, the probability would change depending on which total you chose.

Yes, the general probability is different than the probability for a specific number, just like throwing 2 dice

With 2 dice you can have results from 2 (1+1) to 12 (6+6), but the results for a specifc number could vary from 1/36 (for example 2 which has only one combination) to 6/36 for a 7. 7 is the most likely result, made up of any of 1+6,2+5,3+4,4+3,5+2,6+1.

(Isn't probability interesting? It seems easier than calculus, but in fact can really play havoc with your head!)


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

#10 2006-08-23 06:59:09

ace_stac
Guest

Re: Calculating Odds

tongue but if u were a real mind reader u wud of read da mind of sum1 hu is good at maths and seen their answer, dat wud hav bin more impressive big_smile

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