# Thread: Probability of many coin flips coming up heads 65% etc.

1. ## Probability of many coin flips coming up heads 65% etc.

Hello, I am wondering how to calculate what the probability would be of flipping a coin, say, 250 times and having it come up heads 65% of the time. Or 500 times and 90%. Maybe I should be asking how to calculate if it will be at LEAST 65%, at least 90%, etc. I am very interested in this problem.

Thanks a lot.

2. ## Re: Probability of many coin flips coming up heads 65% etc.

You will want to investigate the binomial distribution for this problem.

EDIT: Where the number of trials n is large and the per-trial probability p does not differ hugely from 0.5, you can use the normal approximation to estimate the probabilities you’re after with good accuracy.

3. ## Re: Probability of many coin flips coming up heads 65% etc.

http://stattrek.com/online-calculator/binomial.aspx
here is an online automatic calculator for you. Just fill in the probability of success (0.5), number of trials (250), number of successes (65% x 250 = 162.5 -> 163).
AT LEAST = P (X >=163)

4. ## Re: Probability of many coin flips coming up heads 65% etc.

See my web pages on the subject:
http://home.ptd.net/~artnpeg/RUNS.html

5. ## Re: Probability of many coin flips coming up heads 65% etc.

Thanks a lot people this is awesome.

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