Calculating the Probability of Flipping a Coin 100 Times

[cloud squall]

how would you figure out what the chances are of flipping a coin 100 times and it landing 50 times of heads and 50 on tails in no particular oredr?

 

[Hurkyl]

Divide the total number of ways one can get 50 tails and 50 heads in 100 flips by the number of possible outcomes of 100 flips.

 

[cloud squall]

well how would you find all the possables?>

 

[Hurkyl]

Have you heard of combinations and permutations?

The numerator of the ratio is the number of ways you can choose exactly 50 out of the 100 experiements to be tails

As for the denominator of the ratio, there are two outcomes for each experiment and 100 experiments... do you know how to find the total number of possible outcomes?

 

[mathman]

binomial expansion

The general term in a binomial expansion is
p^k.q^(n-k)n!/(k!.(n-k)!),
where k is the number of successes in n trials, p is the probability of success on one trial and q=1-p. I am using . for multiplication.

In your problem n=100, k=50, and p=1/2, where success is heads (this is arbitrary).

 

[Hurkyl]

I fail to see how any of your post, sol1, is relevant to the topic. You really should start your own thread when you want to talk about your theories instead of hijacking other threads.

 

[Verasace]

Flip a coin true probability and relevance

This is my first post to this board so I hope I am on the right thread for this question...

Concerning coin flip probabilities...

In my graduate undergrad & grad stat classes I learned the probability of getting heads or tails is 50/50.

But I have something to toss out into the ring for comment...

According to my limited research, the 50/50 probability appears to be a mean probability, and that the actual probability is relevant upon previous coin flips in order to obtain an mean 50/50 probability.

For example, if out of 10,000 coin flips, I get 9000 heads, then for the next 10,000 flips, the distribution of heads vs. tails would not be 50/50, but would be weighed in favor of more tails in order to get back to the 50/50 mean.

I call such a change in normal tendency as "probability pressure" (PP)on the "probability wave" (PW). I realize the term probability wave is already established in reference to light, but it seems to apply here.

If one graphs the results of 10,000 coin tosses (or 100,000 as I have), giving heads a value of +1 and tails a value -1, one can easily visualize the PW and should be able to recognize the strength of the PP, either positive or negative, seems to increase the greater the distance from the mean “score” of 0 the wave extends.

Considering the range from the crest of one wave to the next, and the distance between the crests, one may theorize that at the peak of each wave the odds are not truly 50/50, but are skewed.

One may also see that there appears to be a limiting factor on the actual height, or frequency, of the wave, as the possible range for 10,000 tosses could theoretically be a score of 10,000 (100%) either positive or negative, but I have not observed a variance of more than about 3%.

A question I have yet to solve is developing a formula to determine the true probability of a coin toss when relevancy is considered. It appears that the higher, or lower, the score from the mean probability, the greater the skew from 50/50, perhaps on some type of ratio.

Any thoughts, suggestions, comments

 

[Verasace]

A new thread

Sorry, but I think I now realize I probably should have started a new thread, so please disregard my previous post on this thread and refer to it on the new thread "Coin flip true probability and relevance"

Again, sorry

 

[sol1]

Originally posted by Verasace
Sorry, but I think I now realize I probably should have started a new thread, so please disregard my previous post on this thread and refer to it on the new thread "Coin flip true probability and relevance"

Again, sorry

Good idea

Oh I think you are on the right track. Check out Bell Curve, or soliton, Bec condensate, and then maybe you can tell me how this was possible? Probable outcomes, has to have some certainty, so like in orbital configrations how is shape determined. Strings are most help consider the zero point particle really is a particle that never comes to rest, yet we are able to discern the relevanc eof tis energy in the ways I have mentioned, yet this is a energy determination? What is uncertainty in energy detrminations and we raise the question about gravity in this world . Now we see probability in ways we had not considered? Heisenberg's uncertainty principles are confronted here?

Happy trails

Sol