probOfStreak

Calculate the probability of a run or streak of K consecutive successes in N Bernoulli trials.

% RESULT = PROBOFSTREAK(N, K, P)
% Function to calculate the probability of getting a run or streak of K
% consecutive successes in N Bernoulli trials with probability P. Stated
% otherwise, this calculates the probability of a run or streak of K
% consective heads in N independent coin tosses. N and K are integers where
% N>=0, K>0, and 0<=P<=1.
%
% EXAMPLES:
% Calculate the probability of observing 4 consective heads (successes)
% during 10 coin tosses (trials) using a fair coin (P=0.5):
% result = probOfStreak(10,4,0.5);
%
% Calculate the probability of observing 4 consective heads (successes)
% during 10 coin tosses (trials) using an unfair coin that lands on heads
% 60% of the time (P=0.6):
% result = probOfStreak(10,4,0.6);
%
%
% Algorithm adapted from Javascript code embedded here:
% http://maxgriffin.net/CalcStreaks.shtml
%
% which is an adaptation of the algorithm originally described here:
% http://www.askamathematician.com/2010/07/q-whats-the-chance-of-getting-a-run-of-k-successes-in-n-bernoulli-trials-why-use-approximations-when-the-exact-answer-is-known/
%
% Jeffrey Evans
% January 3, 2012