How many possibilities do we have when...

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ruth26

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Hello, everyone! Thank you in advance for your time. I will try to describe my problem as best as I can.

We have a column with 3000 rows and each row says either W or L. How many different possibilities can this create? I was thinking 2 with an exponent of 3000. Which would give pretty much infinite possibilities. (Not sure if this is even correct. It is just my assumption.)

Now the hard part. What if the W makes an appearance in the range of 50-55% cases and L 45%-50%. (Of course they give only 100% together. So if W finds itself in the column 53% of the time then L has to be the other 47%.)

So I was hoping there would be a mathematical way to find out how many possibilities would this give. Logic tells me there would be less possibilities because the range is now limited (eventhough its not set to just lets say 55% for W and 45% for L but anywhere from 50-55% for W and 45-50% for L. It is still only 5% of the whole spectrum of previous possibilies /or so I think/)

Any thoughts on this subject are appreciated!

ruth
 
ruth26 said:
Hello, everyone! Thank you in advance for your time. I will try to describe my problem as best as I can.

We have a column with 3000 rows and each row says either W or L. How many different possibilities can this create? I was thinking 2 with an exponent of 3000. Which would give pretty much infinite possibilities. (Not sure if this is even correct. It is just my assumption.)

Now the hard part. What if the W makes an appearance in the range of 50-55% cases and L 45%-50%. (Of course they give only 100% together. So if W finds itself in the column 53% of the time then L has to be the other 47%.)

So I was hoping there would be a mathematical way to find out how many possibilities would this give. Logic tells me there would be less possibilities because the range is now limited (eventhough its not set to just lets say 55% for W and 45% for L but anywhere from 50-55% for W and 45-50% for L. It is still only 5% of the whole spectrum of previous possibilies /or so I think/)

Any thoughts on this subject are appreciated!

ruth
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Please read the http://www.freemathhelp.com/forum/announcement.php?f=32 page. What have you done? Even if you think you are wrong, please show us what you have done so that we can find your mistake (if any) or point you toward a solution.

As a hint, suppose your individual W, L event was the toss of a supposedly fair coin (50% heads, 50% tails) with W=heads. You have two outcomes, so in 10 tosses of the coins you would have a possibility of 210 different outcomes and about 50% should be heads (W) and about 50% should be tails (L). Now suppose we examine the outcome and and find 30% W. Does this say something about the fairness of the coin or something else?
 
Well my approach was following -> if there are 3000 rows and lets say the chances are 50% W and 50% L then there are 3000 possibilities where the first W could be and then 2999 where to put the second W etc.. down to 1501 possibilities where to put the last 1500th W so...we put all the remaining Ls in the options that are left. Outcome of this action should be 3000!/1500! for 3000 rows and 50% chance of W and L? The problem is I dont know if this approach is correct. :confused:

Any help is welcome :)
Thank you once again,
ruth
 
Well my approach to this problem was the following - if there are 3000 rows and say the chance of W and L are even at 50% for each. Then we can place the first W at any of those 3000 spots, second at any of those remaining 2999 spots etc.. down to 1501 where we put the last one. And then do the same for the Ls and the outcome would be 3000!/1500!. The problem is I dont know if this approach is correct.:confused:

Any help or advice is welcome!
Thanks again,
ruth
 
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