ProbabilityEssential Math 12

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Name:

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Introduction

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Probability and Odds - Single Event

Probability and Odds - Two and Multiple Event

Experimental and Theoretical Probability

Expected Value (Expected Win/Loss)

(robability in the Workplace

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Calculate the following

12%of2O .12 -°

10%of42 4.z..n

24%of48 ‘

20%of 113

Probability and Odds

02

Essential Math 12

Probability

Introduction

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Percent Fraction Decimal Words

13% 13 0.13 l3outof 100

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Example 1A bag has six balls in it. The colours are as follows: red, green, yellow, orange, black, andwhite, One ball will be drawn from the bag.

entify the event:

Identify all possible outcomes: , ‘ I

Example 2Bob is drawing marbles from a bag: there are 5 green, 3 yellow and 1 red.

a) State the event.

b) State all the possible outcomes; how many possible outcomes,52&3 : 7 LcL—’?5

c) State the probability of drawing a yellow.

O3 33%d) State the odds for drdwing green.

- :e) State the odds against drawing red.) L :

f) What is The probability of drawing green or red?

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Questions - Probability and Odds

1) Given the event, identify all possible outcomes

Rolling a sIx-sided cube (n”) Event:Outcomes: , ‘3,tI,S

Flipping a coin Event: 4’(ipi- tm”

Outcomes:

Spin a spinner with four colours: red, orange, blue, and green.Event: pOutcomes:

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2) If you roll a six-sided cube (die) / 3 ‘ /

a) Calculate the probability of rolling a 2.

Qb) Calculate the probability of rolling an even number.

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c) Calculate the probability of rolling a number greater than 4.

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d) Calculate the probability of not rolling a 6.

3) A spinner has four colours: red, orange, blue, and green.

a) Calculate the probability of not spinning blue.

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b) State the odds for spinning red,

c) State the odds against spinning red.

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d) State the odds for spinning green or blue.

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e) State the odds against spinning green or blue.

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4) The weather forecast states that there is a 30% probability of rain tomorrow.

a) State the odds against it raining tomorrow.

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b) State the odds for it raining tomorrow, Q3O7o

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5) There are ten numbers in a hat numbered lthrough 10. A ball is drawn at random,0 a) Probability of picking an even number

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b) State the odds for picking a 7.

c) State the odds against drawn a numberless Than 3.

s+Ld) State the odds against drawing a number more than 4.

3e) State the odds for drawing a four.

6) The odds of snow this Tuesday is 5:4. Express the probability of it not rqirn as

a) Decimal 0

b) Percent L1(1.

c) FractionC’

7) Identify a situation where the odds are 5:2.

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Odds and ProbabiUty - Two Event & MuItpIe Event

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Make a probability tree and a matrix to make

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Example 1A six-side cube (die) is rolled and a spinner with the colours: orange, yellow, brown and grey

is spun at the same time.

State the event and their individual outcomes

Event 1: Event 2:

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OutcomesforEventi: .OutcomesforEvent2: O.J_?

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Make a probability tree to list all possible outcomes.0

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Example 2There are 4 balls in a hat numbered lthrough 4. A ball is drawn and returned to the hat and

then second ball is drawn.

a list of all outcomes.

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d) State the probability of not spinning red, red?

e) State the odds ef spinning one blue and one red (order does not maffer).

2) A coin is flipped Iwice.

a) State the probability of flipping heads, heads.

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b) State the probability of flipping one head and one tail.

3) Two dice are rolled.

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a) State the probability of rolling 1 and 1 (snake eyes).

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b) State the odds against rolling a sum less than 5.

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a) What is the probabilhy that they will have at least 3 girls?D

b) What are the odds for having 4 children of the same gender?

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4) April and Ryan will have four children.

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Experimental and Theoretical Probability

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Example 1A die is rolled 542 times and a “6” occurs 151 times.

a) State the theoretical probability of rolling a “6”

b) State the experiment probability,

c) Is it possible that “6” is rolled 12 consecutive times?

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Questions - Experimental and Theoretical Probability

1) A coin is flipped 974 times and it has been heads 532 times.

a) State the theoretical probability of flipping a heads.

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b) State the experimental probability of flipping a tails.

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2) You are roll a six-sided cube (die) times, The outcomes of the six rolls are as follows:5, 1,3,5,2,

a) State the experiment probability.

b) State the theoretical probability.

3) The probability of being left handed is approximately 1 in 11. Out of 13,250 how manypeople to you expect to have leff handed.

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4) A cup from Tim Horton’s “Roll up the Rim to Win” contest being a winner isapproximately 1 out 9. Jessica buys 9 cups of coffee and did not get a winner, Sheinsists that the statement 1 out of every 9 cups is a winner must be wrong. Is 1 out ofevery 9 óups correct? Please state your reasoning.

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5) You flip a coin five times and the following occurred: heads, heads, tails, heads,heads.

a) State the experimental probability,

b) What is the probability flipping a heads on the next flip. Explain,/

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6) A quality control specialist at a factory knows that 2% of widgets are defective. On aday he notices that there were 20 of 200 widget made were defective. Should thequality control specialist be concerned that too many widgets are defective? Explain.

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7) Erwin is a farmer in rural Manitoba. The isan equal probabWty that a farmer in Erwin’s

area will plant one of two crops: wheat or âEiWiñiüi7eys 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.

b) State the experimental probability that a surveyed farmer will plant canola.

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C) Explain why Erwin might decide to plant canola even though most farmers in the

area are planning to plant wheat.

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8) State an example where having an item failing 10% of the time is acceptable.

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9) State an example where having an item failing 0.001 % unacceptable.

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Expected Value (Expected Win/Loss)

E(V) = P(win) gain — P(loss) loss

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A card game has five cards, one of which is the winner, The game costs $1.00 to play. If youselect the correct card, you win $4.00. Calculate the expected win/loss. Interpret themeaningofthisnumber. piL)

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achel owns a window cleaning company. She is considering puffing in a bid for acontract. She calculates the expected value to be $425. Interpret the meaning of theexpected value. Should she bid on the contract?

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Questions - Expected Value (Expected Win/Loss)

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b. Pay $1. Draw a card from a shuffled deck, If it is a

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e. Pay $1. Toss Iwo coins. If they are both heads, you win $3.-,

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1) Based on past experience, a building contractor estimates that the probability of

winning a contract is 0.3. The contract is worth $25,000 and she knows it will cost her

$2,400 to prepare a contract proposal. Find the expected win/loss of the contract

proposal. Is it financially a good idea for her to bid on the contract?

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-$ sic2) For each of the following games determine whether you would win, lose, or break

even, if played many times.

a. Pay $1. Toss a coin, If it shows heads, you win $2.

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heart you get $5.?(s ItS;

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c. Pay $2. Draw a card from a shuffled deck, If it is a jack or an ace, you get $10,

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d. Pay$1, Rolladie. lfa2or3shows,youget$4.¶I i -1 1 ri ‘ P( lc5)( (D1

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3) Based on past experience, a systems engineer sets the probability of winning acomputer contract at 0.25. The contract is worth $10,000 and the engineer calculatesit would cost $1,800 to prepare a contract proposal.

a) Find the expected value of the contract proposal. How much will the engineer gain ifhe wins the contract? P(-) -y.. )

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b) Is it financially a good idea for the engineer to bid on the contract? Explain.

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4) A carpet cleaning company uses flyers to promote its business. The company knowsthat on average 1 out of every 100 households receiving its flyer will use its service,

Q One average, the company makes a profit of $50.00 on each household whosecarpets it cleans. It costs the company $0.25 for each flyer.

a. Find the expected value of each flyer.P() ((s) (1s

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b. Find the expected value of 10 000 flyers.

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c. Is it financially a good idea for the company to send out flyers? Please explain

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5) A community club raffles off a $1500 big screen TV. The tickets each cost $5 and therD

are 2500 tickets sold.

a) What is your expected value if you had bought only one of the tickets?

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b) How does the expected value change if you buy five of these tickets? Is it beffer to

purchase more tickets?

6) A manufacturer builds and sells widgets. He know that, on average, 13 widgets per

100 are defective. It costs $12 to build each widget and they sell for $18 each. He

plans on building 100000 this year. Will the manufacturer make or lose money on

widgets this year?

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EDrobability in the Workplace

1) Mr. Morin has 48 students in Essential Math 12. When he is marking, five of the first sixtest all received a mark higher than 90%. Did he make the test too easy? Pleaseprovide rationale.

2) Paul is building a fence and needs 350 usable boards. At the lumber store the probabilitythat a board will be useable is 85%. How many boards should Paul buy? Please explain.

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CD) Nancy is an excellent forklift operator. She has 33 years experience without an accident:her record is flawless. Amy, Nancy’s boss, states “the probability that Nancy will get into anaccident is 0. Evaluate this statement.

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4) Identify when landscaping companies and golf courses use probability in its operation.Please provide rationale,

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5) At the casino, a roulette dealer noticed that the number “22” has occurred 3 times in

a row, He expresses great concern to his boss. Was his concern justified? Explain.

a) Identify when Manitoba Public Insurance uses probability in its business.

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