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Feb21-12, 01:13 PM
P: 206
You are thinking in terms of "unlikely" and your mind is playing a common trick on you. Yes, it is unlikely to spin 7 black in a row. But it is just as "unlikely" to spin brbrbrb or rbrbrbr or brrbrbb as it is to spin bbbbbbb. They are equally likely. Your confusion is in comparing the probability of bbbbbbb to what appears to you to be a "random" sequence. But the question is not "what is the probability of bbbbbbb vs. any of the large number of random sequences that are not bbbbbbb"? The proper question is "what is the probability of bbbbbbb vs. the probability of any other particular sequence"? The answer is that they are all equally likely.