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]