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If you were told I flip a coin 10 times and 9 were heads.

Would it be most logical to assume the other was tails if they're was no reason for it to be heads more often.

I read an article saying more serial killers were born in November and if there is no reason then shouldnt it even out over time?

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    Regarding the serial killers, unless it's _completely even_ (which is very unlikely), _some_ month has to have the most. Might as well be November as any other month. Also, if I am allowed to speculate a bit, there might be some psychological effects at play here, since children born in November and December are often younger (and thus physically smaller and weaker) than all the other kids they interact with throughout their childhood. It has been documented that world-class athletes are commonly born early in the year, and it's speculated to be for that very (or is it "the opposite"?) reason. – 2017-01-21
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    That is an interesting idea, however if it was proven to have no difference should it even out over time to 1/12. And for this would the others have to be higher at some point to achieve this 'real probability'? Or is it most likely that November will always be a bit higher now because the rest are still 1/12 and November is highest as off this moment? @arthur – 2017-01-21
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    This is just going to be idle speculation without more information to back the question up. For instance, what was that article? Where were its statistics from? – 2017-01-21
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    If you flip a fair coin ten times, and it comes up heads the first nine times, then the probability it comes up tails the tenth time is one-half. Coins have no memory – they don't remember what happened the first nine times you flipped them. – 2017-01-22
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    @GerryMyerson is right if you _know_ the coin is fair. How do you tell the difference between a probabilist, a statistician, and a fool? Probabilist says 50:50 on next toss. Statistician begins to suspect an unfair coin and bets the next toss will also be Heads. Fool thinks "It's about time for a Tail," and bets on Tails. – 2017-01-22
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    Good, SRawes. Let me encourage you to write up and post an answer, based on what you now understand. Then, you can accept that answer. – 2017-01-23
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    Even if the number of serial killers were exactly divisible by 12, it is unlikely that every month would have the same number born in that month. We should _expect_ that the distribution would be unequal for a completely random chance. On the other hand, $100$ born in one month and $5$ or fewer in any other month (for example) is also unlikely to happen by chance. So we _don't_ expect it to completely even out over time but we also expect it not to get _too_ uneven. – 2017-01-23

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There is no correlation between a past event and future if it is a truly random event, therefore, the probability will remain $0.5$ (for a two-sided coin).

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    I like the 1st sentence. I don't understand the 2nd one. – 2017-01-24