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Drawing tickets
A box contains tickets marked \(1,2,…,n\). A ticket is drawn at random from the box.
Sampling with replacement — Then the ticket is replaced in the box and a second ticket is drawn at random. Find the probability of the following events:
a) the first ticket drawn is numer 1 and the second is number 2;
b) the numbers on the two tickets are consectutive integers;
c) the second number drawn is bigger than the first number.
Sampling without replacement — The ticket is not replaced in the box and a second ticket is drawn at random.
d) Repeat a)-c).
[Pitman page 9, Problem 3]
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 ?
