probability question

[christopher1]

consider an event that occurs 1/3 times.

what is the chances of the event happening 12 times out of 16, given 1500 trials.

i know theres a simple formula but i cant find it...

 

[FLASH1296]

I assume that you mean 12 out of 16 trials in succession. If that is the case ...

Firstly you need to know the probability of the event occurring once. e.g. 50%

You then need to know how many times a sequence of 16 trials can occur in a
total of 1500 trials. The answer is a number considerably short of 100.

The probability of one occurrence is the probability taken to the12th power.

The probability of the event happening once in all of those sets of 16 times 12 is the answer.

If you meant any 12 out of any series of 16 trials then the probability is far greater.

 

[christopher1]

basically its a binomial distribution where:

probability of event=.33
number of trials=16
number of successes=12

but instead of only 16, we want to 1500 trials and see if 12/16 ever occurs in those 1500. this is where i am hung up and can't find the formula i am looking for, tried google, wikipedia, even a statistics book...

if you consider that there are 93 independent trials in 1500 u can calculate it by taking (1-probability)^93, but this doesnt account for the fact that we arent looking at 93 sets of 16 trials, we are looking at 1500 trials so overlap can occur between the trials.

 

[Nvrlose37]

Not sure if I'm right here but I gave it a shot.

Take 3^16= 43,046,721

After closer looking of the problem, i tried to use the Binomial Coefficient "n choose k" but I believe that would only work in a normal permutation. That is the only thing eluding me is how many possibilities of 12 out of 16 there are.

Also, when you do say 12 of 16, does that mean it must only come out 12 of 16 times or does it mean at least 12 of 16? That would definitely affect it.

I wish I could help more, this was a very interesting question.