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MBF 3CI: Probability Review Question Set
Recall: In a deck of cards, there are 52 cards. Half are black, and half are red. There are two black
suits: “clubs” and “spades”. There are two red suits: “hearts” and “diamonds”. In each suit, there are
3 “face cards”. The face cards are “Jack”, “Queen” and “King”.
1. The graph shows the results of repeatedly drawing one card at random from a deck of
cards, and then replacing it after the outcome is recorded.
a) For how many trials was a card selected from the deck?
b) What is the experimental probability of drawing a black face card
from the deck? Write your answer as a fraction, a decimal, and a percent.
c) Determine the experimental probability of drawing a black numbered card
from the deck. Write your answer as a fraction in lowest terms.
d) Add your answers from parts b) and c) together.
Express the sum as a fraction.
e) Is this result what you expected? Explain.
2. Jessica plays softball. In 25 at-bats she got 14 hits. What is Jessica’s experimental
probability of getting a hit?
Recall:
Theoretical probability =
number of successful outcomes for the event
overall number of possible outcomes
1
, since the overall
6
number of possible outcomes is 6 and the number of ways to successfully get a “5” is only 1.
Suppose you roll a die. The theoretical probability that you roll a “5” is
3. Multiple Choice. If the probability of having rain tomorrow is 60%, what is the
probability of not having rain tomorrow?
A)
B)
C)
D)
4. A fair die is rolled. Determine the theoretical probability that an odd number is
rolled. Write your answer as a fraction in lowest terms.
5. Two fair dice (a blue and red one) are rolled and the sum of the outcomes on the top
of each die is observed. Calculate, in lowest terms:
a) P(sum of 5)
sum
b) P(sum of 5 or sum of 10)
c) P(not getting a sum of 5)
Use the chart on the right to help you.
6. A card is selected at random from a deck of cards. Find the theoretical probability
of each outcome. Express your answer as a fraction in lowest terms.
a) a red face card
b) a black face card that is a male (King or Jack)
c) a numbered card that is an even number (Hint: an Ace is an odd card.)
d) an odd-numbered spade
e) a red ace
7. At a school assembly, there are 100 students in grade 9, 125 in grade 10, 225 in grade
11, and 170 in grade 12. Every student at the assembly entered their name for a door
prize. If selection is random, what is the probability that the prize will be won by
a) a grade 9 student?
b) a grade 11 or 12 student?
c) a grade 12 student, if all grade 11 students are disqualified from winning?
Recall: In a probability experiment, if trials are repeated “again and again,” the experimental
probability will tend to equal the theoretical probability. This is known as the … LAW OF LARGE
NUMBERS. Note: when I say “again and again,” I really mean “thousands and thousands and
thousands of trials!”
8. Multiple Choice. In a probability experiment, a fair coin is flipped (at random)
several times. In the first several trials the outcomes occurred:
“Heads”,
“Heads”,
“Heads”,
The next outcome will be:
A) “Heads”
B) “Tails”
“Heads”,
“Heads”,
“Heads”,
C) impossible to predict since the event is random
9. Multiple Choice. If a fair coin is flipped 25000 times, by the Law of Large Numbers,
one can expect the number of “Tails” to be about:
A) 25000
B) 12500
C) neither A) nor B) are correct
10. A die was rolled 100 times. The results are shown in the table.
a) Determine the experimental probability of each outcome.
b) What is the theoretical probability of each outcome?
c) Could the die be "loaded" (or “unfair”)? Explain.
d) What could you do to verify your conclusion in part c)?
Outcome
1
2
3
4
5
6
Frequency
3
22
6
36
16
17
FINAL ANSWERS
1. a) 200 trials
3
b)
, 0.15, 15%
17
c)
d)
49
20
50
100
e) Yes. The result represents all black cards in a deck of cards, and 49% is close to 50%.
3 1
2
7
8
1
2. 56%
3. B Note: = 40%
4. =
5. a) 9 b) 36 c) 9
5
6
2
3
1
5
5
1
6. a)
b)
c)
d)
e)
26
13
13
52
26
5
34
395
79
7. a)
b)
c)
8. C
9. B
=
620
124
31
79
10. a)
3
;
11
;
3
;
9
;
4
;
17
b)
1
for every outcome.
100 50 50 25 25 100
6
c) Possibly. The numbers 2 and 4 were rolled almost 60% of the time. MORE ANALYSIS IS
REQUIRED. See part d).
d) Based on the Law of Large Numbers, conduct thousands and thousands and thousands of trials to see if
the experimental probability remains different from the theoretical probability; if it does then it is
loaded or unfair. In theory, if the die is rolled thousands of times, each outcome will occur equally as
each other outcome.