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MTHE/STAT 351 — Fall 2016
Practice Problem Set 2
Chapter, section and problem numbers refer to the 3rd edition of the Ghahramani textbook.
1. A number x is selected at random in the interval [−1, 1]. Consider the events A = {x < 0}
and B = {|x − 0.5| < 1}. Find the probabilities of B, A ∩ B, and A ∪ B.
2. Section 2.2, # 9
3. Section 2.3, # 11. Also, what is the probability of at least two dice showing up with the same
face, if only five fair dice were tossed? What is this probability if seven fair dice were tossed?
4. A track coach is trying to choose a good 4 × 100 meter relay team from seven women runners.
How many choices (a relay choice includes the order of the runners) does she have if
(a) there are no restrictions;
(b) Alice and Beth will not run on the same team;
(c) Cathy will run only if she can be the anchor (the anchor is the last person to run on the
relay).
5. A palindrome is a sequence of characters that reads the same forwards and backwards. For
example, “noon”, “level”, “detartrated”, “aeiouoiea” and “012353210” are all palindromes.
Using the 26 lower-case letters of the English alphabet, how many palindromes of length 7
can be made
(a) if there are no restrictions on the number of times each letter may appear?
(b) if no letter can appear more than twice? [For example, “fahehaf”.]
(c) if one letter must appear exactly three times, and the rest no more than twice? [For
example, “fahahaf”.]
6. Section 2.4, # 8.
7. Section 2.4, # 15.