Precalculus with Trigonometry: Concepts and Applications

Paul A. Foerster

Chapter 9

Probability, and Functions of a Random Variable - all with Video Answers

Educators

Section 1

Introduction to Probability

Problem 1

A salesperson has 7 customers in Denver and 13 customers in Reno. In how many different ways could she telephone
a. A customer in Denver and then a customer in Reno?
b. A customer in Denver or a customer in Reno, but not both?

Prashant Bana

Prashant Bana

Numerade Educator

Problem 2

A pizza establishment offers 12 vegetable toppings and 5 meat toppings. Find the number of different ways you could select
a. A meat topping or a vegetable topping
b. A meat topping and a vegetable topping

Sheryl Ezze

Numerade Educator

Problem 3

A reading list consists of 11 novels and 5 biographies. Find the number of different ways a student could select
a. A novel or a biography
b. A novel and then a biography
c. A biography and then another biography

Sheryl Ezze

Numerade Educator

Problem 4

A convoy of 20 cargo ships and 5 escort vessels approaches the Suez Canal. In each scenario, how many different ways are there that these vessels could begin to go through the canal?
(Check your book to see image)
a. A cargo ship and then an escort vessel
b. A cargo ship or an escort vessel
c. A cargo ship and then another cargo ship

Sheryl Ezze

Numerade Educator

Problem 5

The menu at Paesano's lists 7 salads, 11 entrees, and 9 desserts. How many different salad-entree-dessert meals could you select? (Meals are considered to be different if any one thing is different.)

Sheryl Ezze

Numerade Educator

Problem 6

Admiral Motors manufactures cars with 5 different body styles, 11 different exterior colors, and 6 different interior colors. A dealership wants to display one of each possible variety of car in its showroom. Explain to the manager of the dealership why the plan would be impractical.

Sheryl Ezze

Numerade Educator

Problem 7

Consider the letters in the word LOGARITHM.
a. In how many different ways could you select a vowel or a consonant?
b. In how many different ways could you select a vowel and then a consonant?
c. How many different three-letter "words" (for example, "ORL," "HLG," and "AOI') could you make using each letter no more than once in any one word? (There are three events: "select the first letter," "select the second letter," and "select the third letter." Find the number of ways each event can occur, and then figure out what to do with the three results.)

Sheryl Ezze

Numerade Educator

Problem 8

Lee brought two jazz CDs and five rap CDs to play at the class picnic.
a. How many different ways could he choose a jazz CD and then a rap CD?
b. How many different ways could he choose a jazz CD or a rap CD?
c. Lee's CD player allows him to load four CDs at once. The CDs will play in the order he loads them How many different orderings of four CDs are possible? (See Problem 7 for a hint.)

Sheryl Ezze

Numerade Educator

Problem 9

There are 20 girls on the basketball team. Of these, 17 are over 16 years old, 12 are taller than $170 \mathrm{cm},$ and 9 are both older than 16 and taller than $170 \mathrm{cm} .$ How many of the girls are older than 16 or taller than $170 \mathrm{cm} ?$

Sheryl Ezze

Numerade Educator

Problem 10

Lyle's DVD collection includes 37 classic films and 29 comedies. Of these, 21 are classic comedies. How many DVDs does Lyle have that are classics or comedies?

Sheryl Ezze

Numerade Educator

Problem 11

The library has 463 books dealing with science and 592 books of fiction. Of these, 37 are science fiction books. How many books are either science or fiction?

Sheryl Ezze

Numerade Educator

Problem 12

The senior class has 367 girls and 425 students with brown hair. Of the girls, 296 have brown hair. In how many different ways could you select a girl or a brown-haired student from the senior class?

Sheryl Ezze

Numerade Educator

Problem 13

Seating Problem: There are 10 students in a class and 10 chairs, numbered 1 through 10
a. In how many different ways could a student be selected to occupy chair $1 ?$
b. After someone is seated in chair $1,$ how many different ways are there of seating someone in chair $2 ?$
c. In how many different ways could chairs 1 and 2 be filled?
d. If two of the students are sitting in chairs 1 and $2,$ in how many different ways could chair 3 be filled?
e. In how many different ways could chairs $1,2,$ and 3 be filled?
f. In how many different ways could all 10 chairs be filled? Surprising?!

Sheryl Ezze

Numerade Educator

Problem 14

Baseball Team Problem 1: Nine people on a baseball team are trying to decide who will play each position.
a. In how many different ways could they select a person to be pitcher?
b. After someone has been selected as pitcher, in how many different ways could they select someone to be catcher?
c. In how many different ways could they select a pitcher and a catcher?
d. After the pitcher and catcher have been selected, in how many different ways could they select a first-base player?
e. In how many different ways could they select a pitcher, catcher, and first-base player?
f. In how many different ways could all nine positions be filled? Surprising?!

Sheryl Ezze

Numerade Educator

Problem 15

License Plate Problem: Many states use car license plates that have six characters. Some states use two letters followed by a number from 1 to $9999 .$ Others use three letters followed by a number from 1 to 999.
a. Which of these two plans allows there to be more possible license plates? How many more?
b. How many different license plates could there be if the state allowed either two letters and four digits or three letters and three digits?
(Check your book to see image)
c. Assuming there are about 200,000,000 motor vehicles in the United States, would it be possible to have a national license plate program using the plan in part b? Explain.

Sheryl Ezze

Numerade Educator

Problem 16

Telephone Number Problem: When 10 -digit telephone numbers were introduced into the United States and Canada in the 1960 s, certain restrictions were placed on the groups of numbers:
Area Code: 3 digits; the first must not be 0 or $1,$ and the second must be 0 or 1 Exchange Code: 3 digits; the first and second must not be 0 or 1 Line Number: 4 digits; at least one must not be 0
a. Find the possible numbers of area codes, exchange codes, and line numbers.
b. How many valid numbers could there be under this numbering scheme?
c. How many 10-digit numbers could be made if there were no restrictions on the three groups of numbers?
d. What is the probability that a 10 -digit number dialed at random would be a valid number under the original restrictions?
e. The total population of the United States and Canada is currently about 300 million. In view of the fact that there are now area codes and exchange codes that do not conform to the original restrictions, what assumption can you make about the number of telephones per person in the United States and Canada?

Carson Merrill

Numerade Educator

Problem 17

Journal Problem: Update your journal with things you have learned about probability and about counting outcomes.

Trent Speier

Numerade Educator