³1username³2³2name³2text_default³2version³21³2ts³2982276706³2ip³2209.66.79.109³2data³2newauthor³31³3minor³30³3text³3The Binomial distribution can be described as the sum of a specific number of independent trials, each of which results in either a zero or a one with constant probability. It provides a reasonable description of coin tossing experiments, among others.

To get a result of X heads in a sequence of N tosses, several things have to happen. If the probability of a head on a single trial is p and the probability of a tail is q (1-p), then X heads and N-X tails has a probability calculated by multiplying X p's times N-X q's or (p^X q^(N-X)). However, there are many sequences which match this description. By the methods of CombinaTorics, we can find that there are N!/X!/(N-X)! different combinations with X heads and N-X tails. So, the probability of X heads is 

   N!/X!/(N-X)! p^X q^(N-X)

[http://netdial.caribe.net/~rabeldin/Home.html RABeldin]
³3summary³3*³2tscreate³2982276706³2keepts³2982364155³2id³21272³2host³2cobrand.bomis.com³2revision³21³1username³2RoseParks³2name³2text_default³2version³21³2ts³2982364155³2ip³2209.66.79.109³2data³2text³3The Binomial distribution can be described as the sum of a specific number of independent trials, each of which results in either a zero or a one with constant probability. It provides a reasonable description of coin tossing experiments, among others.

To get a result of X heads in a sequence of N tosses, several things have to happen. If the probability of a head on a single trial is p and the probability of a tail is q (1-p), then X heads and N-X tails has a probability calculated by multiplying X p's times N-X q's or (p^X q^(N-X)). However, there are many sequences which match this description. By the methods of CombinaTorics, we can find that there are N!/X!/(N-X)! different combinations with X heads and N-X tails. So, the probability of X heads is 

   N!/X!/(N-X)! p^X q^(N-X)

[http://netdial.caribe.net/~rabeldin/Home.html RABeldin]----
First q=1-p, but more important your formula the probabilty of X heads out of N trials is WRONG.
See BinomialDistributuin/Revisited
RoseParks
³3minor³30³3newauthor³31³3summary³3*³2tscreate³2982276706³2keepts³2982365719³2id³21015³2host³2cobrand.bomis.com³2revision³22³1username³2RoseParks³2name³2text_default³2version³21³2ts³2982365719³2ip³2209.66.79.109³2data³2newauthor³30³3minor³30³3text³3The Binomial distribution can be described as the sum of a specific number of independent trials, each of which results in either a zero or a one with constant probability. It provides a reasonable description of coin tossing experiments, among others.

To get a result of X heads in a sequence of N tosses, several things have to happen. If the probability of a head on a single trial is p and the probability of a tail is q (1-p), then X heads and N-X tails has a probability calculated by multiplying X p's times N-X q's or (p^X q^(N-X)). However, there are many sequences which match this description. By the methods of CombinaTorics, we can find that there are N!/X!/(N-X)! different combinations with X heads and N-X tails. So, the probability of X heads is 

   N!/X!/(N-X)! p^X q^(N-X)

[http://netdial.caribe.net/~rabeldin/Home.html RABeldin]----
First q=1-p, but more important your formula the probabilty of X heads out of N trials is WRONG.
See BinomialDistribution/Revisited
RoseParks
³3summary³3*³2tscreate³2982276706³2keepts³2982366272³2id³21015³2host³2cobrand.bomis.com³2revision³23³1username³2RoseParks³2name³2text_default³2version³21³2ts³2982366272³2ip³2209.66.79.109³2data³2text³3The Binomial distribution can be described as the sum of a specific number of independent trials, each of which results in either a zero or a one with constant probability. It provides a reasonable description of coin tossing experiments, among others.

To get a result of X heads in a sequence of N tosses, several things have to happen. If the probability of a head on a single trial is p and the probability of a tail is q (1-p), then X heads and N-X tails has a probability calculated by multiplying X p's times N-X q's or (p^X q^(N-X)). However, there are many sequences which match this description. By the methods of CombinaTorics, we can find that there are N!/X!/(N-X)! different combinations with X heads and N-X tails. So, the probability of X heads is 

   N!/X!/(N-X)! p^X q^(N-X)

[http://netdial.caribe.net/~rabeldin/Home.html RABeldin]----
To the author:
First q=1-p, but more important your formula the probabilty of X heads out of N trials is WRONG.
See BinomialDistribution/Revisited
RoseParks
³3minor³30³3newauthor³30³3summary³3*Will the real author please stand up?³2tscreate³2982276706³2keepts³2982437599³2id³21015³2host³2cobrand.bomis.com³2revision³24³1username³2RoseParks³2name³2text_default³2version³21³2ts³2982437599³2ip³2209.66.79.109³2data³2newauthor³30³3minor³30³3text³3The Binomial distribution can be described as the sum of a specific number of independent trials, each of which results in either a zero or a one with constant probability. It provides a reasonable description of coin tossing experiments, among others.

To get a probability of getting X heads in a sequence of N tosses, several things have to happen. If the probability of a head on a single trial is p and the probability of a tail is q=(1-p) Then the result of X heads and N-X tails on any one trial has a probability calculated  by finding the product of multiplying p times itself X times (p^X), and q times itself (N-X) times (q^(N-X)) giving (p^X q^(N-X)). However, there are many sequences which match this description. By the methods of CombinaTorics, we can find that there are N!/(X!*(N-X)!) different combinations with X heads and N-X tails. So, the probability of X heads is 

   N!/(X!*(N-X)!) p^X q^(N-X)

[http://netdial.caribe.net/~rabeldin/Home.html RABeldin]----
To the author:
First q=1-p, but more important your formula the probabilty of X heads out of N trials is WRONG.
See BinomialDistribution/Revisited
RoseParks
³3summary³3*Well I changed it, since you won't.³2tscreate³2982276706³2keepts³2982437727³2id³21015³2host³2cobrand.bomis.com³2revision³25³1username³2RoseParks³2name³2text_default³2version³21³2ts³2982437727³2ip³2209.66.79.109³2data³2text³3The Binomial distribution can be described as the sum of a specific number of independent trials, each of which results in either a zero or a one with constant probability. It provides a reasonable description of coin tossing experiments, among others.

To get a probability of getting X heads in a sequence of N tosses, several things have to happen. If the probability of a head on a single trial is p and then the probability of a tail is q=(1-p) Then the result of X heads and N-X tails on any one trial has a probability calculated  by finding the product of multiplying p times itself X times (p^X), and q times itself (N-X) times (q^(N-X)) giving (p^X q^(N-X)). However, there are many sequences which match this description. By the methods of CombinaTorics, we can find that there are N!/(X!*(N-X)!) different combinations with X heads and N-X tails. So, the probability of X heads is 

   N!/(X!*(N-X)!) p^X q^(N-X)

[http://netdial.caribe.net/~rabeldin/Home.html RABeldin]----
To the author:
First q=1-p, but more important your formula the probabilty of X heads out of N trials is WRONG.
See BinomialDistribution/Revisited
RoseParks
³3minor³30³3newauthor³30³3summary³3*You won't change this, so I did.³2tscreate³2982276706³2keepts³2982437860³2id³21015³2host³2cobrand.bomis.com³2revision³26