Bernoulli-Consecutive-Toss

This is an application of Kolmogorov Zero-One Law in the case of Bernoulli consecutive tosses.

Let P(Heads) = p and consider infinitely many independent tosses. Let A_k be the event that k or more consecutive heads occurs amongst the tosses numbered 2^k,...,2^k+1-1. Then, if p is greater than or equal to 1/2 then P(A_k i.o.) = 1 and if p < 1/2 then P(A_k i.o.) = 0.

We simulate the process described above. The program plots a series of scatterplots with probabilities varying from 0 to 1 in increments of 1/20 (set to default).