MPM4U0
Chapter 4 and 5 Worksheet
Venn diagrams, combinations, probability, odds.
1. For S, the set of letters in the word S T A N D A R D I Z A T I O N,
A, the set of vowels in the word S T A N D A R D I Z A T I O N,
B, the set of letters in the word S T A N D A R D,
list a)
A B
b)
A B
c)
n  B  S  d)
n S  A 
2. Find the indicated values for the given sets.
S = { desk, table, armchair, wardrobe, stool, coffee table, dresser }
D = { stool, dresser, coffee table, armchair }
E = { desk, dresser, stool, table, wardrobe }
a) n(S)
b) n(D)
c) n(E)
d) n(D ∩ E) e) n(D ∪ E).
3. The travel club has 17 members.
a. In how many ways can seven members be chosen to go to Rome?
b. In how many ways can eight members be chosen for this trip if Adam, Natasha
and Hillary have to go because they speak Italian?
4. For S, the set of letters in the word M U L T I C U L T U R A L I S M,
A, the set of vowels in the word M U L T I C U L T U R A L I S M,
B, the set of letters in the word C U L T U R A L,
list a) A  B
b) A  B c) B  S .
5. Find the indicated values for the given sets.
S = { red, green, white, blue, gold }
D = { green, red }
E = { blue, gold, white }
a) n(S) b) n(D) c) n(E) d) n(D ∩ E) e) n(D ∪ E).
6. Evaluate each expression:
7 
4 
a).
18
C13
b). C ( 12, 9)
12

8
c). 
5 8 
8 5 
7. Show that      .
8. How many different heads-tails scenarios can be arranged using 6 coin?
9. Parents are purchasing Christmas gifts. There have been some suggestions from
family members: their daughter Emily requests three gifts, their son Philip expects
four gifts, their grandparents expect one gift each, and the parents have been
planning to buy two gifts for each other. Because of unexpected budget restrictions
(no Christmas bonus), they may not be able to buy all of these. How many different
possible purchases could they make?
10. A survey of consumers conducted by a local hardwood store produced the
following data:
- 90% have some walls painted
- 50% have some wallpaper
- 65% have wall tiles
- 40% have paint and wallpaper
- 30% have wallpaper and wall tiles
- nobody has wallpaper only
Construct a Venn diagram to determine:
a. What percent of those surveyed have wall tiles only?
b. What percent of those surveyed have tiles and painted walls?
c. What percent of those surveyed have exactly two types of walls?
11. A school librarian is purchasing books. Altogether there have been requests from
staff members for two copies of Webster’s Dictionary, six copies of The English
Writer’s Style Manual, four copies of The Cambridge FactFinder , and three copy
of The History of Mathematics. Because of budget restrictions, he may not be able
to buy all of these. How many different possible purchases could he make?
12. In how many ways can 8 students be selected from a group that consists of 14
male and 20 female students if the group must contain at least three girls?
Use both, direct and indirect methods.
13. In how many ways can 7 people be selected from a group that consists of 8 adults
and 10 children if the group must contain at least two children?
Use indirect method.
14. Rewrite each of the following using Pascal=s formula.
12
a).
C 6  12 C 5
b). C(15, 7) - C(14, 6) c).
 15  14
   
 10  10
15. Determine the probability of:
a. tossing at least one tails with three different coins
b. rolling a number not greater than 3 with one die
c. not drawing a 7 or 8 from a standard deck of cards
d. rolling a number greater than 5 with two dice when points are multiplied
e. selecting non-green tie from a closet containing 3 black, 7 white, and
11 green ties
16. Probability of event D is 0.65. What are odds in favour of and against event D?
17. Determine the odds in favour of choosing each of the following while selecting
two random numbers from 1 to 3
a. at least one 3
b. two 3 or two 2
18. Calculate probability:
a. P(B|A) if P(A and B) = 0.12 and P(A) = 0.6
b. P(A and B) if P(B|A) = 0.45 and P(A) = 0.6
19 Calculate probability of:
a. choosing randomly either a spade or a king from a standard deck of cards
b. tossing an odd number or prime number with one die (1 is not a prime number)
20. Suppose the odds of the Toronto Argonauts winning the Grey Cup are 3:14, while
the odds of the Ottawa Renegades winning the Grey Cup are 4:21. What is greater:
the probability of not winning the Grey Cup by the Argonauts or by the Renegades?
21. Carl, Barb, Ann and Dave are going to the theater. They are taking separate buses
from 4 different locations. What is the probability that:
a. they will not arrive in age order?
b. the two ladies will arrive first or last?
22. The probability that Pat will go to Middle Ontario University is 30%. The probability
that she will go to Eastern University is 45%. If Pat goes to Middle, the probability
that her sister Maddy go to Eastern is 75%. What is the probability of each of the
following.
a. Pat does not go to university.
b. Pat and Maddy attend different universities
23. Mohamed noticed that the performance of his baseball team depends on the
outcome of the previous game. When his team won, there was an 70% chance
that they would win the next game. If they lost, there is only a 40% that they would
win their next game.
a. What is the probability that they lose the next game?
b. Following a win, what is the probability that Mohamed’s team will win the third
game?
24. Calculate probability of:
a. rolling an even number or number greater than 16 with two dice when numbers
are multiplied
b. tossing at least one tails or at least one heads with two different coins.
25. What is the probability of drawing two aces from a well-shuffled standard deck
of cards?
26. What is the probability of randomly choosing 3 female students from a class of
12 female and 11 male students?
27. Refer to ex. 9. What is the probability that both the children will receive at least
one gift each?