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 |
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)), that is (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) |
N!/(X!*(N-X)!) p^X q^(N-X) |
[RABeldin] |
[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 |
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)), that is (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)