Math 1116, Homework #6, Spring 2013
Name ________________________________________
Instructions: Answer the following questions on separate numbered page(s) and attach work to this
page. Indicate for each problem on this sheet which page the answer to the question can be found, and
indicate the answers clearly in your work (you can circle the answer, for instance).
1. For each question below, find the number of situations described. Check that the number is a
whole number.
a. The number of ways to choose three cards from a standard deck? What if there are two
jokers added?
b. The number of ways to roll a 6-sided die 5 times.
c. The number of ways to choose a 4-letter password.
d. The number of 4-letter passwords if you can only use the letters QRSTU allowing repetition.
Without repetition.
e. If a dancing class has 24 students (12 males, 12 females), how many different ways can you
make dancing partners if each pair must contain one male and one female.
f. Standard format license plates for cars in Ohio contains a group of three letters, followed by
a group of four numbers. Find the number of different license plates of that type in the
state.
g. In California, they have 9 positions on their license plates instead of seven. If every position
could be a letter or a number, how many different license plates does California have?
h. Suppose you are asked to enter a password for a new computer account using both capital
and lower case letters, numbers, and the 32 special characters available on the standard
computer keyboard. How many possible passwords are there if it’s 8 digits long? What if
it’s 13 digits long?
i. If a boy owns two pairs of pants, 3 shirts, 8 ties and 2 jackets, how many different outfits can
he have if he must wear one of each?
j. If there are 5 players in a weighted voting system, how many total coalitions are there?
(Hint: You will have to consider the number of coalitions with all five players, the number
with four, the number with three, etc. Don’t be concerned with the weights of their votes,
just the numbers of coalitions of each size.)
k. The number of ways first, second and third place can be award among 210 contestants.
l. The number of ways three vacations can be awarded among 210 contestants.
2. For each question below, find the probability associated with each situation described. Check
that each value is between 0 and 1 (inclusive).
a. In a hat are small slips of paper, each with one letter of the alphabet on them.
i.
Find the probability of drawing a vowel from the hat.
ii.
Find the probability of drawing a consonant from the hat.
iii.
The probability of three letters being chosen in the order consonant, vowel,
consonant.
b. The probability of getting a 5 on a six-sided die.
c. The probability of getting a 4 on an icosahedral die.
d. The probability of getting a number other than 8 on a dodecahedral die.
e. The probability of getting a number less than 3 on a six-sided die.
f. The probability of rolling a 1 on a six-sided die, followed by a 6.
g. The probability of rolling two six-sided dice and getting a sum equal to 7
h. Given the table:
A
B
C
Total
Male
8
18
13
39
Female
10
12
4
26
Total
18
30
17
65
i.
Find the probability that a student was female.
ii.
Find the probability that the student was both female and got a C.
iii.
Find the probability that a student got an A.
i. The probability that a card chosen from a standard card deck will be a king or a queen.
j. The probability that you will choose, from a standard card deck, a king, and then a queen.
k. The probability you will choose, from a standard card deck, the jack of diamonds followed
by the ace of clubs. What is the probability this won’t happen?
l. From a jar with 32 blue marbles and 14 white ones, what is the probability you will pull two
red ones in a row? Two white ones in a row?
3. A friend devises a game that is played by rolling a six-sided die once. If you roll a 6, he pays you
$3, if you roll a 5 he pays you nothing, if you roll a number less than 5, you pay him a $1.
Compute the expected value for this game. Should you play this game?
4. In a lottery, a player picks six numbers from 1 to 23. If the player matches all six numbers he
gets $30,000. Otherwise, they lose $1. Find the expected value of this game.
5. Recalculate #4 with figures for a real lottery, like PowerBall. You need to look up the number of
numbers you are choosing from, the pay-off if you win, and the cost of a ticket to play.
6. If the odds of an event are given below, compute the probability.
a. The odds against the event are 7 to 2.
b. The odds for the event are 3 to 5.
7. Given the probability of an event below, compute the odds.
a. The probability of the event is 3/7.
b. The probability against an event is 2/11.