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The binomial distribution gives the frequencies of "successes" in a fixed number of independent "trials". Use this tag for questions about data that might be binomially distributed or for questions about the theory of this distribution.
3
votes
Probability of a run of k successes in a sequence of n Bernoulli trials
Here is a Mathematica simulation for the Markov chain approach, note that Mathematica indexes by $1$ not $0$:
M = Table[e[i, j] /. {
e[9, 1] :> 0,
e[9, 9] :> 1,
e[_, 1] :> (1 - p),
e[ …