JonF writes:
I predict that if you toss a fair coin 1,000 times half of them will come up heads.
Er, the probability of that is 9.3326E-302 not 1.
Something near to half of them will come up heads, but the probability of any one specific outcome is 1/2 raised to the power of the number of trials.
Actually 9.33x10
-302 is the probability of a specific sequence. What you actually want is the sum of the probabilities of all 1000 toss sequences where precisely 500 heads appear. The probability of each sequence is 9.33x10
-302, but how many such sequences are there? I believe there are 1000!/(500!*500!) such sequences, and multiplying this by 9.33x10
-302 you get around 0.025. So the odds of getting exactly 500 heads after 1000 tosses is about 2.5%.
--Percy
Edited by Percy, : Fix math typo.
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