# Thread: probability of 8 successes out of 256 events

1. ## probability of 8 successes out of 256 events

Hi all hope you are well, i was trying to calculate what the probability of getting exactly 8 successes in 256 events. I used a Binomial on line calculator but the result just didnt look right

There are 2 outcomes so it is like a coin toss so put these values in

Probability of success on a single trial - 0.5
Number of trials - 256
Number of successes (x) - 8

and got the result - 3.53792472330638E-63

if the sequence is broken then we start from 1 again so H,H,H,H,H,T is a lossing sequence and we start again from 1 but 6 of the 256 tries has been used now

Hope this makes sense

Thank you

2. ## Re: probability of 8 successes out of 256 events

If I understand your question correctly, you want to know the probability of getting at least eight consecutive successes in a run of up to 256 trials, where the probability of a success on a single trial is 0.5. Is that correct?

If so, it would mean that the run ends as soon as either (1) you have eight consecutive successes, or (2) you have done 256 trials. Is that also correct?

3. ## Re: probability of 8 successes out of 256 events

Yes that is correct.thank you

4. ## Re: probability of 8 successes out of 256 events

Also I would like to know probability that at least on series of 8 consecutive success occur when all 256 events are completed. Thank you

5. ## Re: probability of 8 successes out of 256 events

HI Can anyone help me with this if not can you suggest another forum that might be able to answer my question. Thank you

6. ## Re: probability of 8 successes out of 256 events

The probability is 0.391316, which is borne out by a Monte Carlo simulation of over 100,000,000 trials.

The probability generating function is:

with

and

.

You want .

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