Question: Sampling with and without replacement.
A box contains tickets marked 1, 2, .... N. a ticket is drawn at random from the box. Then this ticket is replaced in the box and a second ticket is drawn at random. Find the probabilities of the following events:
a) the first ticket drawn is number 1 and the second ticket is number 2:
b) the numbers on the tow tickets are consecutive integers, meaning the first number drawn is one less than the second number drawn,
c) the second number drawn is bigger than the first number drawn.
Sampling without replacement:
d) Repeat a) through c) assuming instead that the first ticket drawn is not replace, so the second ticket drawn must be different from the first.