# Probability of a consecutive event over (x) trials?

How do I calculate the chance/probability of an event with a 35% chance of success occurring 5 times in a row over the course of (x) number of trials?

So over 100 trials how many consecutive 5 successes are there? 1,000 trials? 1 million trials?

### 1 Answer

- davidLv 74 weeks agoFavorite Answer
The answer depends on the 'rules' for selecting. --- Selection with replacement or without replacement.

Ex .. Cards ... If I select a card from a standard deck and then do not put the card back before selecting another card .. that is is seletion without replacement === But if you select a card, look at it, then put it back in the deck before selecting the next .. that is selection with replacement.

... flipping a coin is selection with replacement .. if you get heads then the next time you can still get either h or t.

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Assuming you have some kind of selection with replacement the 35% means probabiity of success each and every time is 0.35

P 5 successes in a row = (0.35)^5 <<< use a calculator = 0.0052522

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So over 100 trials how many consecutive 5 successes are there? <<< this is ambiguous..

. I will guess that you mean EXPECTED.

... the answer is

0.0052522 X 96 = 0.5042 .... not even one time is expected.

And specifically it would be a roulette wheel scenario, I.e. how many spins = a high probability that 5 successes in a row happens at that 35% (

Specifically 0.351351351351351)