Probability Problems:
1. The sides of a wooden cube each have a different letter written on them. The letters are a, c, e, g, i,
and k. The cube is then rolled twice. Are event V, at least one vowel comes up, and event C, at least
one consonant comes up, complementary. Explain your answer.
2. Six chocolates of identical appearance are placed on a tray. There are three with hazelnut cream (H),
two with raspberry jelly (R), and one with coffee cream (C). Ms Sweet selects one first. She then
decides to take another. Determine whether the event M, the chocolates selected are of the same
flavour, and event D, the chocolates selected are of different flavours, are complementary. Give the
reasons for your answer.
3. In a drawer, there are seven sheets of wrapping paper: four green (G) sheets, two blue (B) sheets and
one red (R) sheet. The sheets are handed out at random: one to Laurie, one to Evelyn, and one to
Benedict. Are the event A, the three sheets handed out are the same colour, and the event Z, the three
sheets handed out are different colours, complementary. Why?
4. Three cyclists are riding individually along a bicycle path. At the first intersection, the main path
branches off into three different paths: path 1 for beginners, path 2 for intermediate cyclists and path 3
for expert cyclists. Thus each cyclist can choose the path that suits him best. Using this information,
state whether event P, at least one cyclist selects path 3 and event Q, the three cyclists select paths 1
or 2, are complementary. Explain your answer.
5. After the first snowfall, 23 cars are already parked in the parking lot of a garage specializing in tire
installation, before opening time. There are 7 white cars, 2 green cars, 8 red cars, 5 grey cars and 1
blue car. The manager decides to hold a draw to determine the order in which the customers will be
served. He writes down the registration numbers of the cars on pieces of paper, which he places in an
empty box.
a)
b)
c)
d)
e)
f)
g)
h)
Determine the probability that the first customer served owns a blue car.
What is the probability that the first customer served owns a red car?
Calculate the probability that the first 2 customers served own a green car.
Calculate the probability that none of the first three customers served own a red car.
Calculate the probability that the first 5 customers served own grey cars.
What is the probability that none of the first 5 customers served own a grey car?
Calculate the probability that the first 4 customers served do not all own a white car.
What is the probability that at least one of the first 6 customers served owns a red car?
6. Each employee in a plant is identified by a code composed of three letters followed by three numbers.
Note that all of the letters and numbers are selected at random and that the same letter or number may
appear more than once in a code.
a)
b)
c)
d)
What is the probability that the code assigned to John Paul Townsend starts with his initials,
JPT?
Determine the probability that Denise Corcoran’s code contains the number 8 at least once.
Calculate the probability that Patrick Smith’s code is composed only of vowels and uneven
numbers.
What is the probability that Anne Cochrane’s code contains no number under 3?
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William Low
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7. A furniture chain is about to open three new stores in a large city. The owners will randomly select in
which area of the city their respective stores will be located. North (N), South (S), East (E), or West
(W). Mr. Brown has first choice, followed by Ms. White and, lastly, Mr. Green. Determine whether
the following events are complementary: event X, no store in the west (W) end, and event Y, one store
in the north (N) end and one store in the south (S) end. Explain your answer.
8. The four aces in a deck of playing cards are placed face down on a table. They are the ace of hearts
(), the ace of diamonds (), the ace of clubs (♣) and the ace of spades (♠). First, one of the cards on
the table is selected. A coin is then tossed to obtain tails (T) or heads (H), and then another card is
selected from the remaining cards. Are event D, selecting the ace of hearts () and obtaining tails
(T) in the toss, and the event E, obtaining heads (H) in the toss, complementary? Explain your
answer.
9. At present, there are four roads leading from town T to town U (roads 32, 48, 36, and 16) and five
roads leading from town U to town V (roads 68, 70, 88, 64 and 94). A sixth road, road 52, is under
construction between town U and town V.
68
32
70
48
88
T
U
V
64
36
94
16
52
a) Mr. Laverne must go from town T to town V. He chooses his route at random. What is the
probability that he will drive along roads 48 and 64 in order to get from town T to town V?
b) What would his probability be if road 52 was complete?
10. Adeline and her grandmother are playing cards. Adeline is the first to play and she draws four (4)
cards from the deck.
a) Determine the probability that Adeline drew only red cards.
(N.B. A deck of 52 cards contains 26 black cards and 26 red cards).
b) What is the probability that Adeline drew no face cards?
(N.B. There are 12 face cards in a deck of 52 cards).
c) Calculate the probability that Adeline drew at least one clubs card.
(N.B. There are 13 clubs in a deck of 52 cards).
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11. In the waiting room of a dental clinic, leaflets with crossword puzzles are distributed to patients who
want them. On each sheet, there is one (1) crossword puzzle to be completed. Some of the crossword
puzzles are for beginners, others are for experts, and still others are for individuals with average
puzzle-solving skills. The sheets are placed in no particular order in a pile, without any regard for
level of difficulty. One of the patients, Mr. Graham, asks the receptionist for four (4) puzzle sheets.
The pile contains 63 sheets, 27 of which are printed with beginner-level puzzles, 21 with intermediatelevel puzzles and 15 with expert level puzzles.
a)
b)
c)
What is the probability that Mr. Graham will be given only expert-level puzzles?
What is the probability that Mr. Graham Mr. Graham will be given at least one beginner-level
crossword puzzle?
What is the probability that Mr. Graham will be given no expert-level crossword puzzles?
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