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The coin has been tossed three times each showing up head.The probability of getting head the fourth time should be one half but should be we instead saying it 1/16 considering the previous tosses?

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    $\begingroup$ Consider how the previous flips influence the next flip. Do they? $\endgroup$ – Dave Nov 17 '19 at 13:50
  • $\begingroup$ No. Imagine I gave you a coin and you toss it once. The probability of landing heads is $1/2$, right? And now I tell you that before I handed you the coin I tossed it 100 times. Do you now think that the probability of heads in your toss $1/101^2$? And what if the cashier I got the coin from tossed it a few times? Or thousands of times? $\endgroup$ – corey979 Nov 17 '19 at 14:23
  • $\begingroup$ The coin can't remember anything. It doesn't know what happened last toss, or the last 100 tosses. How could the previous tosses make a difference? Also see... en.wikipedia.org/wiki/Gambler's_fallacy $\endgroup$ – Glen_b Nov 18 '19 at 2:59
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If I understand your question correctly you are asking whether the 4th toss is dependent on the first 3 - the answer is no. Every toss is independent, so the probability of a fair coin landing on heads will be always 0.5. Note that it is perfectly normal to get "clusters" of the same side (e.g. heads showing up x times in a row) given that you toss the coin "enough" times.

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