Worksheet: Probability Review
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[17 subjective questions not graded]
Worksheet: Probability Review
Short Answer
1. Carrie is a kicker on her rugby team. She estimates that her chances of scoring on a penalty kick
during a game are 75% when there is no wind, but only 60% on a windy day. If the weather
forecast gives a 55% probability of windy weather today, what is the probability of Carrie scoring
on a penalty kick in a match this afternoon?
RESPONSE:
ANSWER:
NOTES:
REF:
Applications
Problem
2. Use a tree diagram to explain why the probability that a family with four children has either all girls
or all boys is , assuming that the probability of having a boy equals the probability of having a girl.
RESPONSE:
ANSWER: Two of the sixteen branches represent outcomes with either four boys or four girls.
Each of the sixteen outcomes is equally likely, so the probability of having all girls or
all boys is
.
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NOTES:
REF:
file:///P:/Ms. Sediako/MDM4U/Probability_Review.htm
Applications, Communication
3. A stable has 15 horses available for trail rides. Of these horses, 6 are all brown, 5 are mainly white,
and the rest are black. If Jasmine selects one at random, what is the probability that this horse will
a) be black?
b) not be black?
c) be either black or brown?
RESPONSE:
ANSWER:
a)
b)
c)
NOTES:
REF:
Applications
4. Tom is practising archery with a target has three concentric zones: a circular bull’s-eye in the
centre, an inner ring, and an outer ring. He has an 0.12 probability of hitting the bull’s-eye, an 0.37
probability of hitting the inner ring, and an 0.43 probability of hitting the outer ring. On an given
shot, what is the probability that Tom
a) misses the target?
b) hits the target but does not get a bull’s-eye?
c) hits the inner ring or the bull’s-eye?
RESPONSE:
ANSWER:
a)
b)
c)
NOTES:
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REF:
file:///P:/Ms. Sediako/MDM4U/Probability_Review.htm
Applications
5. The Royals’ coach stated that “the odds in favour of us winning the next game are 5:7, the odds of
tying the next game are 1:3, and the odds of losing the next game are 2:3.” Can the coach’s
predictions be correct? Justify your answer.
RESPONSE:
ANSWER: The coach is incorrect.
If the odds are 5:7 in favour of winning, then
If the odds are 1:3 in favour of tying, then
If the odds are 2:3 in favour of losing, then
These three probabilities add to
.
.
.
, which is impossible, since probabilities of all
possible outcomes is always 1.
NOTES:
REF:
Communication, Thinking/Inquiry/Problem Solving
6. Explain how you would calculate the tomorrow’s “probability of precipitation” if the odds against
precipitation tomorrow are 4:1.
RESPONSE:
ANSWER:
If the odds against having rain are 4:1, then the probability of not having rain is .
Therefore, the probability of precipitation must be
NOTES:
REF:
, or 20%.
Applications, Communication
7. Explain why odds of 4 to 5 in favour of an event occurring have a different meaning than the same
event having a probability of .
RESPONSE:
ANSWER:
The odds of 4 to 5 mean that the event has a probability of . Thus, odds of 4 to 5
are quite different from a probability of .
NOTES:
REF:
Communication
8. Suppose you randomly draw two marbles, without replacement, from a bag containing six green,
four red, and three black marbles.
a) Draw a tree diagram to illustrate all possible outcomes of this draw.
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b) Determine the probability that both marbles are red.
c) Determine the probability that you pick at least one green marble.
RESPONSE:
ANSWER: a)
b)
c)
NOTES:
REF:
Applications
9. A six-member working group to plan a student common room is to be selected from five teachers
and nine students. If the working group is randomly selected, what is the probability that it will
include at least two teachers?
RESPONSE:
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ANSWER:
NOTES:
REF:
Applications
10. Len just wrote a multiple-choice test with 15 questions, each having four choices. Len is sure that
he got exactly 9 of the first 12 questions correct, but he guessed randomly on the last 3 questions.
What is the probability that he will get at least 80% on the test?
RESPONSE:
ANSWER: A score of 80% requires getting 12 out of the 15 questions right. If Len answered 9
out of the first 12 questions correctly, he can score 80% only if he guessed all 3 of
the remaining questions correctly.
Therefore Len has only about a 1.6% chance of getting 80% on the test.
NOTES:
REF:
Applications
11. Leela has five white and six grey huskies in her kennel. If a wilderness expedition chooses a team
of six sled dogs at random from Leela’s kennel, what is the probability the team will consist of
a) all white huskies?
b) all grey huskies?
c) three of each colour?
RESPONSE:
ANSWER: a) The probability is 0 since there are only 5 white huskies available.
b) Since there are 11 dogs altogether, the team can be chosen in
ways.
However, there are only 6 grey huskies, so there is only one way of picking an all
grey team. The probability of randomly selecting this team from the 11 dogs is
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c)
NOTES:
REF:
Applications
12. Six friends go to their favourite restaurant, which has ten entrees on the menu. If the friends are
equally likely to pick any of the entrees, what is the probability that at least two of them will order
the same one?
RESPONSE:
ANSWER: This question is similar to the birthday problem in Example 3 on p.323 of the student
textbook.
If none of the friends pick the same entree, there are
ways to select their meals.
The probability of this event is
Therefore, the probability that at least two will order the same entree is 1 – 0.1512 =
0.8488, or about 84.9%.
NOTES:
REF:
Applications
13. A study on the effects that listening to loud music through headphones had on teenagers’ hearing
found that 12% of those teenagers in the sample who did listen to music in this way showed signs of
hearing problems. If 60% of the sample reported that they listened to loud music on headphones
regularly, and 85% of the sample were found not to have hearing problems, are the events {having
hearing problems} and {listening to loud music on headphones} independent? Explain your
reasoning.
RESPONSE:
ANSWER: If events A and B are independent,
.
Since P(hearing problems) = 0.15 and P(listening to loud music on headphones) =
0.60, then
However, the observed probability of having hearing problems and listening to loud
music on headphones is 0.12, which is significantly higher than 0.09. Therefore,
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these two events cannot be independent if the survey results are accurate.
NOTES:
REF:
Communication, Thinking/Inquiry/Problem Solving
14. If a committee of six is to be chosen randomly from nine grade-11 students and seven grade-12
students, what is the probability that the committee will be either all grade-12 students or all
grade-11 students?
RESPONSE:
ANSWER:
NOTES:
REF:
Applications
15. Explain the difference between mutually exclusive events and independent events using an
example of each to illustrate your answer. In your explanation, show why probabilities are added
for a mutually exclusive set of events and are multiplied for independent events.
RESPONSE:
ANSWER: Answers may vary. Students should make the key point that mutually exclusive
events cannot occur at the same time, while some independent events can. The
probability of an independent event is not affected by the occurrence of other
events.
NOTES:
REF:
Communication
16. If a survey on teenage readers of popular magazines shows that 38% subscribe to Teen People,
47% subscribe to Cool Life, and 35% subscribe to neither magazine, what is the probability that a
randomly selected teenager
a) subscribes to both magazines?
b) subscribes to either one magazine or both?
c) subscribes to only one of the two magazines?
RESPONSE:
ANSWER:
a) Using a Venn diagram,
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b)
c)
NOTES:
REF:
Applications, Communication
17. A survey of 50 female high-school athletes collected the following data.
Team
Field hockey
Volleyball
Rugby
Both rugby and field hockey
Both rugby and volleyball
Both field hockey and
volleyball
All three teams
Number of Athletes
23
16
29
8
9
7
6
a) Draw a Venn diagram to illustrate the above data.
b) Determine the probability that a randomly selected athlete from this sample will play either
rugby or field hockey.
c) What is the probability that a randomly selected athlete will play on only one of the three sports
teams?
d) Determine the probability that a randomly selected rugby player also plays volleyball.
e) Determine the probability that a randomly selected athlete who does not play rugby is on the
field-hockey team.
RESPONSE:
ANSWER: a)
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b) Only 6 athletes do not play either field hockey or rugby. Therefore, the
probability of selecting an athlete who plays either sport is
= 0.88.
c) From the Venn diagram, 38 athletes play on only one of the three sports teams.
Therefore, P(only one team) =
, or 0.76.
d) Venn Diagram Method
The Venn diagram above shows that 9 volleyball players also play on the rugby
team. Therefore,
.
Conditional Probability Method
e) Venn Diagram Method
The Venn diagram above shows that 15 out of the 21 athletes not on the rugby
team play field hockey. Therefore,
Conditional Probability Method
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NOTES:
REF:
file:///P:/Ms. Sediako/MDM4U/Probability_Review.htm
Applications, Communication
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