Category Archives: Typical vs Atypical

Balls in boxes

A box contains 1000 bulbs, of which 2 are black and the rest are white.

  1. Which of the following is mostlikely to occur in 1000 draws with replacement from the box ? Fewer than 2 black balls, Exactly two black balls, more than two black balls.
  2. If two series of 1000 draws are made at random from the box, what is, approximately, is the chance that they produce the same number of black balls ?

 

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]