Sample 2 Chapter 13 Test #2 PreCalculus 2 Name___________________________
1. Let A = {11, 12, 14, 17, 22} B = {22, 24, 26, 28}. Find the elements in the set A  B .
Given the Venn Diagram
2. How many are in A?
U 51
A
25
3. How many are in A or C?
B
19
32
15 12
18
28 C
4. How many are in A and B?
5. If n( A)  55, n( B)  95, and n( A B)  93, find n( A B)
6. In a survey of 900 students, 400 were registered in Pre-Calculus, 600 were registered in
Computer Science, and 300 were registered in both courses.
a. How many students were registered in Pre-Calculus or Computer Science?
b. How many were registered in neither course?
8. In how many ways can 4 people be assigned to serve as President, Vice-President,
Secretary, and Treasurer from the junior class of 900 students?
9. In the Olympics, with about 800 swimmers competing, all with equally likely chance of
winning, how many ways could they finish 1st, 2nd, and 3rd ?
10. How many seven-digit phone numbers can begin with 847?
11. In how many ways can a committee consisting of 5 faculty members and 4 students be
formed if 60 faculty members and 100 students are eligible to serve on the committee??
12. How many 3 or 4 digit numbers are there that contain no 1’s or 2’s?
13. How many different 10 letter words (real or imaginary) can be formed from the letters
in the word BASKETBALL?
14. A group of 75 people is going to be formed into committees of 20, 12, and 10 people.
How many committees can be formed if:
a. A person can serve on any number of committees?
b. No person can serve on more than one committee?
15. In how many ways can a committee of 8 professors be formed from a department
having 28 professors?
16. A fair coin is tossed 24 times. Find the probability that exactly 7 heads appear.
17. A coin is weighted so that tails is ten times as likely as heads to occur. What probability
should we assign to tails?
18. Determine the probability of having 2 girls and 2 boys in a 4–child family.
19. A traffic engineer is counting the number of vehicles by type that turn into a residential
area. The table below shows the results of the counts during a four-hour period. Construct
a probability model for the data.
Type of vehicle
Car
SUV
Van
Small truck
Large truck
Response
19
32
7
5
6
Probability
20. If there are 7 people in a room, what is the probability of :
(365 days in a year)
a) no two people having the same birthday?
b) at least two people having the same birthday?
21. A fair coin is tossed 2000 times. Find the probability that exactly 7 tails appear.
22. How many 3 of a kind hands consisting of 4 cards are possible from a deck of 52 cards?
23. A carton of eggs contains 9 cracked eggshells. If you randomly pull out 3 eggs to make
an omelette, what is the probability that both are cracked?
24. In how many ways can 30 volunteers be assigned to 30 booths for a charity bazaar?
25. In 1990 the stock market took big swings up and down. A survey of 900 investors asked
how often they tracked their portfolio. The table shows the investor responses. What is the
probability that an investor tracks their portfolio weekly?
How frequently
Daily
Weekly
Monthly
Couple times a year
Don’t track
response
800
50
40
7
3
26. A special UN committee consists of 20 U.S. representatives, 30 Canadian
representatives, and 15 French representatives. In how many ways can a delegation be
formed using 3 representatives from each country?
27. A person has 9 different math books, 8 different science books, 2 different literature
books, and 6 different history books that they want to arrange on a shelf. In how many
ways can this be done if the books are grouped by subject.