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Balls in boxes
A box contains 1000 bulbs, of which 2 are black and the rest are white.
- 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.
- 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.
- Without calculations, say which of these outcomes is more likely. Why ?
- Confirm your answer to the previous question by a calculation.
[Pitman, p. 108 #3]
