>You are correct, each event is independent. On any flip of a coin there is a 50% change that it will be heads...
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>But, there is also the probablity of the repeating events... flip a coint once, you have a 50/50 chance it will be heads. Flip it again, there is a 50/50 change it will be heads. Let's say it was heads 3 times in a row, what is the probability that it will be heads a fourth time?
For example, the probability of having heads 4 times in a row is 1/16. This probability, calculated as (1/2)^4, is based precisely on the (reasonable) assumption that each event is independent of the other events, that is, that with each flip of the coin, the probability is 1/2, independent of what happened previously.
>Sure, there is still a 50/50 chance of heads on that fourth flip? However, the chance of 4 heads in a row is alot lower than three heads and a tail.
This is basically because there is only one combination that gives you 4 heads. Let 1 = heads, 0=tail, then the only combination is 1111.
Three heads and one tail can be achieved in four different ways: 1110, 1101, 1011, 0111.
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