Category Archives: Drawing with replacement

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.

  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 ?