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Coin Flips: typical behavior

A fair coin is tossed repeatedly. Considering the following two possible outcomes:

55 or more heads in the first 100 tosses.
220 or more heads in the first 400 tosses.

  1. Without calculations, say which of these outcomes is more likely. Why ?
  2. Confirm your answer to the previous question by a calculation.

 

[Pitman, p. 108 #3]

 

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