A fair coin is flipped $10^6$ times.

What's the probability that the number of heads is at least 499000 and at most 501000?

I'm not sure how to even go about starting this. Does it involve the $Q$ function?

  • $\begingroup$ Hast thou studied the binomial distribution, by any chance? $\endgroup$ – dfeuer Oct 7 '13 at 2:59
  • 1
    $\begingroup$ Look also at the normal approximation to the binomial distribution. Them numbers be large. $\endgroup$ – dfeuer Oct 7 '13 at 3:05
  • $\begingroup$ Thanks. This is mostly what I was looking for. Found a video that explains it pretty well. $\endgroup$ – user2503227 Oct 7 '13 at 3:12

By the central limit theorem, the distribution may be well approximated by a normal distribution. The mean $\mu = 10^6 (1/2) = 500000$, and the variance is $\sigma^2 = 10^6 (1/2) (1/2)$ so that the standard deviation is $\sigma = 500$. You are then asked the probability of being within $\pm 2$ standard deviations of the mean.

  • $\begingroup$ Or punch the exact binomial distribution into, say, ghci, and get the exact rational answer quickly enough :P $\endgroup$ – dfeuer Oct 7 '13 at 3:12

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.