Stat 330 (Spring 2015): Homework 2
Due: January 30, 2015
Show all of your work, and please staple your assignment if you use more than one sheet. Write your name,
the course number and the section on every sheet. Problems marked with * will be graded and one additional
randomly chosen problem will be graded. Must show work for full credit.
1. * For all of the following problems, find the sample space first. Determine the size of the sample space,
then deal with the specified event.
(a) A lottery has 53 numbers from which seven are selected without replacement. You play the lottery
by selecting seven numbers from the same 53 numbers without replacement. What is the probability
that your seven numbers are the same as the lottery’s?
(b) Find the probability of being dealt three kings in a five-card hand in a 52-card standard deck when
the cards are drawn without replacement?
(c) How many different passwords of length 6 can be generated from the set of letters ‘a’-‘z’, ‘A’-‘Z’,
and the digits ‘0’, ‘1’-‘9’ using at least two digits? Symbols can be used more than once.
(d) How many ways are there to arrange the letters C I N C I N N A T I to different ”words” of length
10? How many 5 letter words can be made with all 5 letters different?
2. The first three digits of a university phone exchange are 452. If all the sequences of the remaining
four digits are equally likely, what is the probability that a randomly selected university phone number
contains seven distinct digits?
3. Suppose license plates have 6 entries. The first three entries must be letters (A-Z), and the last three
must be digits (0-9). Letters and digits can be used more than once. A license plate is selected randomly.
What is the probability that the letters O, I, and Z and the digits 0 and 1 were not used for this plate?
4. A committee consists of five Caucasians, three Hispanics, two Asians, and two African-Americans. A
subcommittee of four is formed at random.
(a) What is the probability that all ethnic groups are represented in the subcommittee?
(b) What is the probability of at least one non-Caucasian member being in the subcommittee?
5. Suppose you receive 13 cards from a well-shuffled standard deck of cards. What is the probability that
your hand will contain 2 or more Aces?
6. * Baron 2.14
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