Essential Mathematics: Student Booklet (January...

Essential Mathematics: Student Booklet (January 2013)

DI 6. You are given the data set: 1, 2, 3, 4, 5.

\ A) Express the probability of the number 2 being randomly selected from the set. (1 mark)

2- 2o 1

B) Express the probability of not selecting the number 5 from the set. (1 mark)

1 Mark

7. The probability of an event occurring is 3 out of 5. Express this probability as a decimal or percent.

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40


Explain what it means if an event, such as a game or a business contract, has an expected value of 0.

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9 On a quiz out of 10 marks, the scores of several students were: 3, 4, 6, 7, 7, 8, and 10. Express the odds that a randomly selected student scored greater than 50% on the quiz.

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1 Mark

10. The odds against an event occurring are 1:5. Express the probability for the event occurring.

3 Marks

OP 11. A company knows that 1 out of every 100 vacuums sold will be defective in some way. A store sells 100 of these vacuums and 10 people return them because they are defective.

A) Express the experimental probability of buying a defective vacuum. (1 mark)

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• B) Explain the difference between "theoretical probability" and "experimental probability". • (2 marks)


2 Marks

12. A manufacturing plant is concerned with controlling the quality of its products. It was determined that the probability of producing a defective product is 1%.

An employee takes two products from the plant and finds that one of them is defective. The employee is worried that 50% of the products are defective. Explain whether this employee is justified in being worried by these results.

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3 Marks

Essential Mathematics: Student Booklet (June 2013)

29. A fair coin is tossed four (4) times and the results are: heads, heads, heads, tails.

A) Express the probability of the coin landing on "heads" the next time it is tossed. (1 mark)

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B) Explain your answer in Part A. (1 mark)

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30.. In a book, 17 out of 68 pages contain an image. Express the probability, in the form of a fraction, a decimal, and a percent, that a randomly selected page will contain an image.

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Decimal:

Percent


3 Marks

31. Sandy pays $5 to play a game. The probability of winning is 60%. She will receive $10 if she wins.

A) Determine the expected value for this game (2 marks)

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B) Explain whether Sandy should play this game, based on your answer in Part A (1 mark)

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32. Describe a situation that would have favourable odds of 5 : 2.

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Essential Mathematics: student Booklet (June 2013)

3 Marks

33. John has a six-sided cube and each face is labelled with a different number: 1, 2, 3, 4, 5, and 6.

He tosses the cube and sees the following results: 6,4, 6, 6, 1, 6.

A) Assume that the cube is fair. Express the theoretical probability of tossing the cube and it showing a 6. (1 mark)

• B) Express the experimental probability of tossing the cube and it showing a 6. (1 mark)

7

C) Explain whether you think this is a "fair cube". (1 mark)

Essential Mathematics: Student BooHet (June 2013)

1 Mark

34. Express the probability of there being an October snowstorm somewhere in Manitoba if the odds for this occurrence are 3 to 1.


7. State the probability of "two out of five" as a decimal number and as a percent.

decimal number:

percent:

4 Marks

8. The probability that John will get a construction contract is 0.33. It will cost him $25 000 to prepare his bid and, if he gets the contract, it will be worth $100 000.

A) Determine his expected value. (3 marks)

B) Justify whether he should bid on the job, based on your answer in Part A. (1 mark)

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2 Marks

9. Explain the difference between odds and probability.

2 Marks

10. The City of Selkirk is planning a Fun Day.

A) The probability of it raining on Fun Day is 3 out of 24. State the odds that it will not rain on Fun Day. (1 mark)

B) The odds for winning a prize at Fun Day are 2:1. State the probability of winning a prize (1 mark)

Jo

1 Mark

-1-1-1 (January 2014:

3 Marks

11. Erwin is a farmer in rural Manitoba. There is an equal probability that a farmer in Erwin's area will plant one of two crops: wheat or canola. Erwin surveys 10 farmers in the area and finds out that 7 of them plan to plant wheat.

A) State the theoretical probability that a surveyed farmer will plant wheat. (1 mark)

B) State the experimental probability that a surveyed farmer will plant canola. (1 mark)

C) Explain why Erwin might decide to plant canola even though most farmers in the area are planning to plant wheat. (1 mark)

0ii i 12. A fair six-sided cube numbered from 1 to 6 is rolled. State the probability that a 4 or less (1, 2, 3, or 4) will be rolled.


2 Marks

18. The first day of the month falls on a Sunday 48 times in 28 years.

A) State the probability of the first day of any given month falling on a Sunday. (1 mark)

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B) State the odds in favour of this happening (1 mark)

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19. The probability of an eagle returning to the same nest year after year is 8

2 Marks

A) State this probability as a decimal. (1 mark)

B) State the probability of the eagle not returning to the same nest. (1 mark)

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21. Choose the letter that best completes the statement below.


20. The Cook Construction Company is bidding on a $200 000 contract to apply gravel on the roads in the Rural Municipality of Timber Valley. It costs the company $5250 to draft the bid. This company has a 10% chance of winning the contract.

Calculate the expected value of the Cook Construction Company's bid.

Probability compares the number of favourable outcomes to

a) the likelihood of it not occurring

b) the total number of outcomes

c) the number of unfavourable outcomes

d) the likelihood of it occurring

Answer:

1 Mark

22. The odds against hitting a moose on the highway are 193 : 7. State the probability of hitting a moose.

Essential Mathematics: Student Booklet (June 2014).

2 Marks

23. Eagle Motors has determined that the theoretical probability of a vehicle breaking down is 0.001. In a sample of 5000 vehicles, 100 have broken down.

A) State the experimental probability of an Eagle Motors vehicle breaking down. (I mark)

o

B) State the number of vehicles, from the 5000 sampled, that can be expected to break down based on the theoretical probability. (1 mark)

Essential Mathematics: Student Booklet (January 201!

2 Marks'

. The probability of Billy scoring a basket is 6 out of 8. State Billy's success rate as a fraction and as a percent.

Fraction:

Percent:

2 Marks

Jonas is experimenting with pulling blocks out of a bag. There is an equal number of red blocks, yellow blocks, and blue blocks

A) State the theoretical probability of pulling out a yellow block. (I mark)

B) After repeating the experiment several times, Jonas pulled a red block 7 times, a yellow block 3 times, and a blue block 2 times. State the experimental probability of pulling a yellow block. (1 mark)

Essential Mathematics-: Student Booklet (January 2015)

It would cost $1000 for a contractor to bid on a construction project. There is a one in four chance that she will win the contract. If she is awarded the contract she will be paid $3000 for the work.

A) Calculate the expected value (3 marks)

5

B) Justify whether she should bid on the contract based on the expected value calculated in Part A. (1 mark)

1 Mark

10. The weather forecast states that there is a 30% probability of rain for tomorrow. State the odds against it raining tomorrow.

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2 Marks

11. The manager of a clothing company collects the following sales data for the winter season.

T-shirt colours Red Yellow Green Blue

Number purchased 111 140 204 145

A) State the probability that a customer purchased a green T-shirt based on the sales data presented above. (1 mark)

B) The manager of the store needs to order 9000 T-shirts for next year. State how many green T-shirts the manager should order based on the above sales data. (1 mark)

Essential Mathematics: Student Booklet pone 2015)

7. There are 12 red and 28 blue marbles placed in a box.

A) State the probability of randomly selecting a red marble. (1 mark)

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B) State the odds against choosing a red marble. (1 mark)

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1 Mark

8. State the probability of randomly choosing the letter "B" from the letters in the word "probability."

PROBABILITY

Essential Mathematics: Student BooWet (June 2015)

4 Marks

9. Howard spends $1.55 on each food sample he gives away at his restaurant. There is an 8% chance that after tasting the sample, the customer will order the new menu itun. Howard earns $20 for every new menu item he sells.

A) Determine the expected value of the food sample. (3 marks)

B) Justify whether Howard should be offering the food samples based on the expected value (1 mark)

EssenUal Mathematics: Student Booklet (June 2015)

3 Marks

10. Random testing of golf balls shows that 100 out of every 5000 are defective.

A) State the odds in favour of a golf ball being defective. (1 mark)

B) State the probability of a golf ball not being defective. (1 mark)

C) A company produces 80 000 golf balls. State the expected number of defective golf balls. (1 mark)

Essential Mathematics: Student BooWet (June 2015

2 Marks

11. The Teddy Bear Factory hosts birthday parties where children can build their own teddy bears. They offer 4 different party packages that are equally likely to be chosen. Their sales during the last month were as follows:

Red package: 18 Blue package: 34 Green package: 16 Yellow package: 12

A) The Smith family would like to book a party. State the experimental probability that the Smith family will choose the yellow package. (1 mark)

B) State the theoretical probability that the Smith family will choose the yellow package. (1 mark)


C.D4t, Emerito has to write a math quiz at the end of every week. Each quiz is out of 10 marks. His marks on the last 6 weeks' quizzes were as follows:

4 7 8 6 8 7

State the probability that a randomly chosen quiz has a mark of 70% or more.

8. State 63% as a fraction and as a decimal.

Fraction:

Decimal: , J


4 Marks

9. A company wishes to advertise a new type of breakfast cereal by sending out small samples through the mail to potential customers. There is a 7% chance that a potential customer will like the cereal and buy a full box for $6.00.

A) Calculate the expected value for the company if the samples cost $0.40 each to produce and distribute. (3 marks)

B) justify whether the company should try this form of advertising based on your answer in Part A. (1 mark)


10. State the probability of a baseball player hitting a ball given that the odds for this event are 1:4.

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11. Ten cards, numbered 1 to 10, are placed in a bag. A student pulls a card from the bag, records the number, and puts the card back in the bag. The student repeats this process 9 more times. The table below shows the results.

N

6 4 N) 10 6

2

5

A) Smte the experimental probability of a student pulling out a card with a number greater than 7. (1 mark)

B) State the theoretical probability of a student pulling out a card with a number greater than 7. (1 mark)

Essential Mathematics: Student Book! (January 2016)

1 Mark


The probability of a tadpole surviving to become an adult frog is 90%. The odds against this happening are.

a) 1 : 9

b) 9 : 1

c) 1 : 10

d) 10:1

Answer:

Essential Mathematics: Student BooWet (June 2016)

7. Josephine has placed 3 white, 5 blue, and 6 purple marbles in a bag.

A) State the probability of randomly selecting a purple marble from the bag. (1 mark)

(3

B) A purple marble is pulled out of the bag and not replaced. State the probability of randomly selecting another purple marble from the bag. (1 mark)

(c)

1 Mark

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8. State the odds in favour of a tidal wave occurring given that the probability for this event is 3 out of 147.

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4 Marks

9. A game at a summer carnival costs $2 to play. The prize at this game is a stuffed animal valued at $10. The probability of winning the game is 27%.

A) Calculate the expected value (By) for the game from the player's perspective. (3 marks)

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B) Justify whether the owner of the game should continue offering it at the carnival based on your answer in Part A (1 mark)

10. State the probability of "13 out of 50" as a decimal and a percent.

Decimal: 61,26,

<776 Percent:


1. A group of 30 students were given 4 choices and asked to choose their favourite colour. The results were as follows:

Red Blue Yellow Green

9 12 6 3

The teacher states "If I choose a student at random, there is a 25% probability that their favourite colour is green."

The teacher's claim is an example of theoretical probability. Justify the teacher's claim

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1 Mark


Sharon would like to borrow a specific book from the local library. The odds against the book being available are 1: 99. The probability of the book being available is:

a)

b)

c)

d)

2 98

99 1

1 100

99 100

Answer:

Question 7 2 marks 110

4

State the probability of 43% as a fraction and a decimal.

Fraction: /00

Decimal: 4-13

Question 8 11 2 marks

A sports store sells lacrosse sticks. Out of 500 sold, 55 are defective. The manufacturer says that 5 out of 100 is the expected number of defective sticks.

A) State the theoretical probability of a stick being defective. (1 mark)

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B) State the experimental probability of a stick being defective (1 mark)

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12 FssPntial Mathematics: Student Booklet (January 2017)

e Question 9

3 marks 1 13

The probability of winning a computer programming contract is 28%. The contract is worth $12 000 but it costs $2300 to prepare the contract

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Calculate the expected value (EV) of the contract = 5706

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Question 10 2 marks

Given the following spinner:

State the probability of the arrow landing on yellow. (1 mark)

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B) State the odds in favour of the arrow landing on blue. (1 mark)

51 Question 11

1 mark 116

During a hockey season, 75 of the 400 games went into overtime.

State the odds against a game going into overtime.

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(3 /49 QuStiOn 12.

Choose the letter that best completes the statement below.

Probability compares the number of favourable outcomes to the

a) odds for the event

b) odds against the event

c) total number of outcomes

d) theoretical probability

Answer:

1 mark 117

s3 Question 8

2 marks 108

The probability of Jen winning a swimming race is 1 out of 7.

Stare the probability of winning as a decimal and a percent

Decimal: /

/11 0/0 Percent: 29

Question 9 2 marks

The following spinner is divided into 4 colours.

The spinner was spun 40 times and the results are shown in the table below.

Colour Number of Times

green 16 yellow 11 white 8

blue 5

A) State the experimental probability of spinning white. (1 mark)

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B) State the theoretical probability of spinning white. (1 mark)

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8 F-qc-Pntia( Mathematics: Student Booklet (June 2017)

65 Question 10 3 marks III

The probability of a baseball team winning a tournament is 15%.The entry fee is $200. If they win the tournament, the team will receive a rash prize of $1000.

133Ctilik Calculate the expected value (EV). g

EV (0iis)( $8'60) — (o, s'5-)C 209

EV = co

(5) Question 11

2 marks

Alama is the manager of an assembly line that makes compact fluorescent light bulbs. Workers on the assembly line randomly chose 250 light bulbs to test and found 1 defective light bulb.

A) State the experimental probability, in fraction form, of a light bulb being defective. (1 mark)

B) State the number of defective light bulbs that are expected in a shipment of 5000 light bulbs. (1 mark)

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Question 12, 1 mark 114

The odds against hitting a deer on the highway each year are 49 : 1.

State the probability of hitting a deer this year.

Dr 0,02_ 50

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