Problem 1

  1. Can an event A be independent of itself? If so, how?

  2. Say A and B are independent. Are \(A^c\) and \(B^c\) always independent?

Problem 2

There are 10 men and 12 women in a room. Three of them are selected at random to serve on a committee. Find the probabilities that none, one, two or all three of them are women.

Problem 3

Maria flips a fair coin until the first time she gets heads. Let n be the number of flips she needs. If n is an even number Paul flips his coin once, if n is an odd number he flips his coin twice. If we are told that Paul got no heads, what is the probability that Maria got heads on the second try?

Problem 4

In this problem a word is any combination of letters, meaningful or not. In all the problems below you want to use all the letters.

  1. How many words can be made with the letters a,b,c,d?

  2. How many words can be made with the letters a,a,b,c,d?

  3. How many words can be made with the letters a,a,b,b,b,c,d,d?

  4. How many words can be made with the letters a,a,a,b,b,b,c,d if we never want the same two letters next to each other?