Probability Student Outcome: I will be able to write probabilities as ratios, fractions and percents.

• Probability: is the likelihood or chance of an event occurring.• Outcome: any possible result of a probability event.• Favourable Outcome: a successful result in a probability event.

(ex: rolling the #1 on a die)• Possible Outcome: all the results that could occur during a probability

event (ex: rolling a die - - #1, #2, #3, #4, #5, #6)

• P = Favourable Outcomes Possible OutcomesWhat is the probability of rolling the number 2 on a dice?• What is the favourable outcome?• How many possible outcomes?

How to express probability

Student Outcome: I will be able to write probabilities as ratios, fractions and percents.

• Probability can be written in 3 ways...

• As a fraction = 1/6• As a decimal = 0.16

• As a percent

0.16 x 100% = 16%

How often will thenumber 2 show upwhen rolled?

Determine the probabilityStudent Outcome: I will be able to write probabilities as ratios, fractions and percents.

First you must find the possible outcomes (all possibilities)and then the favourable outcomes (what you’re looking for). Then place them into the probability equation.

1. Rolling an even number on a die?2. Pulling a red card out from a deck of cards?3. Using a four colored spinner to find green?4. Selecting a girl from your class?

P = Favourable Outcomes Possible Outcomes

Determine the probabilityStudent Outcome: I will be able to write probabilities as ratios, fractions and percents.

A cookie jar contains 3 chocolate chip, 5 raisin, 11 Oreos,and 6 almond cookies. Find the probability if you were toreach inside the cookie jar for each of the cookies above.

Type of Cookie

Chocolate Chip

Raisin Oreo Almond

Fraction

Decimal

Percent

Ratio

Determine the probabilityStudent Outcome: I will be able to write probabilities as ratios, fractions and percents.

A cookie jar contains 3 chocolate chip, 5 raisin, 11 Oreos,and 6 almond cookies. Find the probability if you were toreach inside the cookie jar for each of the cookies above.

Type of Cookie

Chocolate Chip

Raisin Oreo Almond

Fraction 3/25 5/25 11/25 6/25

Decimal 0.12 0.25 0.44 0.24

Percent 12% 25% 44% 24%

Ratio 3:25 5:25 11:25 6:25

Determine the probability

Page 163-164 # 3, 5, 7, 10

Extend: Page 163 #11, 12

Practical Quiz #1Letter tiles for the word CINCINNATI are placed in a

bag.

a) What is the probability of drawing the letter C?b) What is the probability of drawing the letter N?c) What is the probability of drawing the letter O?

Organized OutcomesStudent Outcome: I will be able to create a sample space involving 2 independent

events.

Independent Events:• The outcome of one event has no effect on the

outcome of another event

• Example: ROCK

PAPER

SCISSORTails Head

ChartStudent Outcome: I will be able to create a sample space involving 2 independent

events.

Sample Space:• All possible outcomes of an event/experiment

(all the combinations) coin

hand

• What is the probability of Paper/Head?• What is the probability of tails showing up?

Sample Space

Head Tail

RockPaperScissor

“Tree Diagram” to represent Outcomes

Student Outcome: I will be able to create a sample space involving 2 independent events.

H T

R P S R P S

Coin Flip

Rock, Paper, Scissor

H, Rock T, Rock H, Paper T, Paper

H, Scissor T, Scissor

Outcomes

“Spider Diagram” to represent Outcomes

Student Outcome: I will be able to create a sample space involving 2 independent events.

RockRock

Paper Paper

Scissor Scissor

Organized OutcomesStudent Outcome: I will be able to create a sample space involving 2 independent

events.

You can find the sample space of two independentevents in many ways.1. Chart2. Tree Diagram3. Spider Diagram

Your choice, but showing one of the aboveillustrates that you can find the favourable andpossible outcomes for probability.

Organized Outcomes

Page 169-170 #5, 8, 9, 10

Extend: Page 170 #13, 14

Probabilities of Simple Independent Events

Student Outcome: I will learn about theoretical probability.

Random: an event in which every outcome has an equal chance ofoccurring.

A school gym has three doors on the stage and two backdoors. During a school play, each character enters throughone of the five doors. The next character to enter can beeither a boy or a girl. Use a “Tree Diagram” to determineto show the sample space. Then answer the questions onthe next slide!

Problem:

Probabilities of Simple Independent Events

Student Outcome: I will learn about theoretical probability.

Random: an event in which every outcome has an equal chance ofoccurring.

See Page 172 for your “Tree Diagram” of the school gymdoors!

Using a Table to DETERMINE Probabilities

Student Outcome: I will learn about theoretical probability.

How to determine probabilities:

Probability (P) = favourable outcomes possible outcomes

= decimal x 100%

Use your results from the “tree diagram” of the gym doorsand place them into a chart. Then determine theprobabilities for the chart.

Using a Table to DETERMINE Probabilities

Student Outcome: I will learn about theoretical probability.

Back Left (BL)

Back Right(BR)

Left Stage(LS)

Centre Stage (CS)

Right Stage(RS)

Boy B-BL B-BR B-LS B-CS B-RS

Girl G-BL G-BR G-LS G-CS G-RS

Determine the probability for the scenarios below...1. Of a boy using any right door?

2. Of anyone (boy or girl) using a stage door?

3. Of a girls using any of the doors?

Determine Probabilities

Page 175-176 #6, 9, 12, 13

Extend: Page 176 #14

Practical Quiz #2On the front of the paper:Draw a sample space using a chart for the following events.On the back of the paper:Draw a sample space using a tree diagram for the following events.

Rolling a 4 sided die and flipping a quarter.

Applications of Independent Events

Student Outcome: I will learn about theoretical probability.

Let’s play “Sit & Save?”(page 177)

RULES:1. Stand up at the beginning of the round.2. Two dice are rolled each round. You may collect the sum of

your dice as long as a “6” does NOT appear. A “6” means all numbers before are cancelled and you get zero for that round.

3. After each roll you have two choices• Continue standing and roll again…hoping for no “6”

OR• Sit and collect your total points!

Applications of Independent Events

Student Outcome: I will learn about theoretical probability.

How can you win at the game of “Sit & Save?”

1. Who had the highest score?2. What is the possibility of a 6 appearing with 2 dice? (sample data)

3. Use the numbers above for each player to find who had the best probability (percent) of not rolling a 6.

Round 1 Round 2 Round 3 Round 4 Round 5

Total

Round 1 Round 2 Round 3 Round 4 Round 5

Round 1 Round 2 Round 3 Round 4 Round 5

Total

Total

Interpret OutcomesStudent Outcome: I will learn about theoretical probability.

Use Tree Diagrams, Charts or other graphic organizers to solveprobability problems.

1. What are the 2 independent events?

2. What is the probability of

the sum of these 2 events adding up to total “4”…

3. What is the probability of outcome having one 3 appear?

Interpret OutcomesStudent Outcome: I will learn about theoretical probability.

1. What is the probability of red appearing?

2. What is the possibility of a black and green appearing?

3. What is the possibility of brown mirror appearing?

Interpret Independent Outcomes

Page 181-182 #4, 6, 8, 9

Extend: Page 182 #11

Theoretical vs. Experimental Probabilities

Student Outcome: I will be able to compare experimental and theoretical probability.

What are the chances of a boy and girl picking the same numberfrom 1-5. Try this 10 times and tally your results (experimental).Then compare to your “theoretical” answer.

BoyGirl

BoyGirlBoyGirlBoyGirlBoyGirl

1 2 3 4 5

Boy B1 B2 B3 B4 B5

Girl G1 G2 G3 G4 G5

experimental

Theoretical

The probability of an event occurring based on experimental results. A tally chart will be required.

The expected probability of an event occurring.

Theoretical vs. Experimental Probabilities

Student Outcome: I will be able to compare experimental and theoretical probability.

You must complete 2 of the 3 activities listed. For each activity you must compare the theoretical and experimentalprobabilities. Each experimental probability must be done 50 times.Then compare to your “theoretical” answer.

Activities 1. Flipping a coin and using a spinner.2. Rolling one 6-sided die and dropping a cup.3. Rolling two 6-sided dice.

Theoretical vs. Experimental Probabilities

Page 187-189 # 4, 6, 7, 9, 11

Practical Quiz #3When these two independent event are done at the same

time, What is the probability of getting:a)anything with red?

b) orange-tails?

Are your ready to be TESTED on “Probability?”

We have covered a lot of material in this unit. Do you have anyconcerns or questions about any of the topics below? 1. Representing probability in different ways… (Pg. 158)2. Types of sample spaces to find the probability (Pg. 166-167)3. Explain how to identify an independent event.4. Determine the outcomes of two independent events. (Pg. 172)5. Find the sum of different events…which sample space would be best to use?6. Solve multiple probabilities… P(1,B) or P(Girls, Boys, 6)7. Use diagrams to interpret data and probabilities. (Pg. 178-179)8. Compare experimental to theoretical probabilities. (Pg. 184)9. Outcome – any possible result of a probability experiment.10. Favourable Outcome – a successful result in a probability experiment.11. Probability – the likelihood of an event happening.12. Random – when every result has an equal chance of occurring.13. Sample Space – all possible outcomes of a probability experiment.14. Tally Chart – an area to record information during experimental probability.

Are your ready to be TESTED on “Probability?”

We have covered a lot of material in this unit. Do you have anyconcerns or questions about any of the topics below?

1. Representing probability in different ways… (Pg. 158)

2. Types of sample spaces to find the probability (Pg. 166-167)

3. Explain how to identify an independent event.4. Determine the outcomes of two independent events. (Pg. 172)

5. Find the sum of different events…which sample space would be best to use?6. Solve multiple probabilities… P(1,B) or P(Girls, Boys, 6)7. Use diagrams to interpret data and probabilities. (Pg. 178-179)

8. Compare experimental to theoretical probabilities. (Pg. 184)

Chapter Review

Page 190 – 191#1-14

Game – Baseball Dice

Handout playing field to students and dice.