Coin Tossing Probability

  • Today, I want to talk about coin toss probability.

    Please imagine that you toss 2000 coins.

    Each coin will fall and rest with either side face up “heads” or “tails” with equal probability.

    Well then, what is the probability that at least 1100 heads appear?

    When I saw this problem for the first time, I thought intuitively the answer is around a few percent.

    However, the actual answer is around 0.0004 percent, and it can be derived easily from a normal distribution.

    This fact implies strong convergence of the probability.

    I wondered the result for a while such as when I’m faced with a paradox, but people with probabilistic sense will understand without much resistance.

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