Any Streak Calculator

Any streak means just that. ANY.

Say a fair coin where Heads and Tails probability of showing is exactly the same. 50%.

Two kinds of outcomes and their total probability = 100%.

That is what this calculator can provide accurate results for.

Another example. A standard six-sided Die (1d6) where all 6 faces have the

same equal probability of showing face up after a random roll.(1 chance in 6)

And the sum of all the probabilities = 100%.

Q1 and Q2 questions have p(Heads) and p(Tails) = 1/2 (50%)

Q3 and Q4 questions have p(all faces) = 1/6 (16.67%)

1. Question: Probability of a run (say Heads) of at least 5 in 20 trials? Answer: 0.2498703 (32751/131072)

2. Question: Probability of ANY run (Heads or Tails) of at least 5 in 20 trials? Answer: 0.4584026337 (240335/524288)

3. Question: Probability of a run (specific. say #1 of fair 1d6) of at least 3 in 30 trials? Answer: 0.06862475057

(250902960984851/3656158440062976)

4. Question: Probability of ANY run (any of 1d6) of at least 3 in a row in 30 trials? Answer: 0.4996127441

(18408557946206617592671/36845653286788892983296)