Transcript Slide 1
Anchor Activity
NDA GAMES DAY • • • • • • • • • • You and a partner will create a game involving some form of probability.
You will need to have rules (explained) What are the possible outcomes ?
How does a player win a game?
What probabilities are important to know? Justify your response.
What strategies might you use to increase your chance of winning? Justify your response.
Speed Gaming will occur If you lose you pay the other player 5 dollars (fake money) This will occur over 2 days.
Teams that collect the most money over 2 days will a trophy!!
Anchor Activity
EXAMPLES OF PROBABILITY GAMES 1. Don’t roll the number (use table) 2. Is it a match? (Page 194)
• • • •
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 Outcomes • • What 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 How often will the number 2 show up when rolled?
As a decimal = 0.16
• As a percent 0.16 x 100% = 16%
Determine the probability
Student 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.
P = Favourable Outcomes Possible Outcomes
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?
Determine the probability
Student 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 to reach inside the cookie jar for each of the cookies above.
Type of Cookie
Fraction
Chocolate Chip Raisin Oreo Almond
Decimal Percent Ratio
Determine the probability
Student 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 to reach inside the cookie jar for each of the cookies above.
Type of Cookie
Fraction
Chocolate Chip
3/25
Raisin
5/25
Oreo
11/25
Almond
6/25
Decimal Percent Ratio
0.12
12% 3:25 0.25
25% 5:25 0.44
44% 11:25 0.24
24% 6:25
Determine
the probability
Page 163-164 3, 5, 9, 10, 11 9 3, 4, 7, 8, 10 1, 4, 6, 7, 8
Practical Quiz #1
Letter tiles for the word CINCINNATI a bag.
are placed in 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 Outcomes
Student 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 SCISSOR Tails Head
Chart
Student 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
Sample Space
Head Tail hand Rock Paper Scissor • • What is the probability of Paper/Head?
What is the probability of tails showing up?
“Tree Diagram” to represent Outcomes
Student Outcome: I will be able to create a sample space involving 2 independent events.
Coin Flip H T Rock, Paper, Scissor R P S R P S
H, Rock H, Paper H, Scissor
Outcomes
T, Rock T, Paper T, Scissor
“Spider Diagram” to represent Outcomes
Student Outcome: I will be able to create a sample space involving 2 independent events.
Rock Paper Scissor Rock Paper Scissor
Organized Outcomes
Student Outcome: I will be able to create a sample space involving 2 independent events.
You can find the sample space of two independent events in many ways.
1. Chart 2. Tree Diagram 3. Spider Diagram Your choice, but showing one of the above illustrates that you can find the
favourable
and
possible
outcomes for probability.
Organized Outcomes
Page 169-170 10 1, 12, 13 1, 4, 5, 7, 8 1, 5, 7, 9, 12
Probabilities of
Simple Independent
Events
Student Outcome: I will learn about theoretical probability.
Random: an event in which every outcome has an equal chance of occurring.
Problem: A school gym has three doors on the stage and two back doors. During a school play, each character enters through one of the five doors. The next character to enter can be either a boy or a girl. Use a “
Tree Diagram
” to determine to show the sample space. Then answer the questions on the next slide!
Probabilities of
Simple Independent
Events
Student Outcome: I will learn about theoretical probability.
Random: an event in which every outcome has an equal chance of occurring.
See Page 172 for your “Tree Diagram” of the school gym doors!
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 doors and place them into a chart. Then determine the probabilities for the chart.
Using a Table to
DETERMINE
Probabilities
Student Outcome: I will learn about theoretical probability.
Boy Girl
Back Left (BL)
B-BL G-BL
Back Right (BR)
B-BR G-BR
Left Stage (LS)
B-LS G-LS
Centre Stage (CS)
B-CS
Right Stage (RS)
B-RS 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 12 13, 14, 15 3, 4, 6, 9, 3, 6, 11, 13
Practical Quiz #2
On 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.
1.
2.
3.
Let’s play “
Sit & Save
?” (page 177) RULES: • • Stand up at the beginning of the round.
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.
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
?”
Round 1 Round 2 Round 3 Round 4 Round 5 Total
1.
2.
3.
Who had the highest score?
What is the possibility of a 6 appearing with 2 dice?
(sample data)
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 Total
Interpret Outcomes
Student Outcome: I will learn about theoretical probability.
Use Tree Diagrams, Charts or other graphic organizers to solve probability 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?
1.
Interpret Outcomes
Student Outcome: I will learn about theoretical probability.
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 9, 10, 11 7 3, 8, 9, 3, 5, 6,
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 number from 1-5. Try this 10 times and tally your results ( experimental ).
Then compare to your “ theoretical ” answer.
experimental
Boy Girl Boy Girl Boy Girl Boy Girl Boy Girl
The probability of an event occurring based on experimental results. A tally chart will be required.
The expected probability of an event occurring.
Boy Girl
1
B1 G1
Theoretical
2
B2 G2
3
B3 G3
4
B4 G4
5
B5 G5
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 experimental probabilities. Each experimental probability must be done 50 times.
Then compare to your “ theoretical ” answer.
Activities 1.
Flipping a coin and using a spinner.
2.
3.
Rolling one 6-sided die and dropping a cup.
Rolling two 6-sided dice.
Theoretical vs. Experimental Probabilities
Page 187-189 7, 9, 11 6 3, 9, 11 1, 3, 4, 8,
Practical Quiz #3
When 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 any concerns or questions about any of the topics below? 10.
11.
12.
13.
14.
6.
7.
8.
9.
1.
2.
3.
4.
5.
Representing probability in different ways… (Pg. 158) Types of sample spaces to find the probability (Pg. 166-167) Explain how to identify an independent event.
Determine the outcomes of two independent events. (Pg. 172) Find the sum of different events…which sample space would be best to use?
Solve multiple probabilities… P(1,B) or P(Girls, Boys, 6) Use diagrams to interpret data and probabilities. (Pg. 178-179) Compare experimental to theoretical probabilities. (Pg. 184) Outcome – any possible result of a probability experiment.
Favourable Outcome – a successful result in a probability experiment.
Probability – the likelihood of an event happening.
Random – when every result has an equal chance of occurring.
Sample Space – all possible outcomes of a probability experiment.
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 any concerns or questions about any of the topics below? 1.
2.
3.
4.
5.
6.
7.
8.
Representing probability in different ways…
(Pg. 158)
Types of sample spaces to find the probability
(Pg. 166-167)
Explain how to identify an independent event.
Determine the outcomes of two independent events.
(Pg. 172)
Find the sum of different events…which sample space would be best to use?
Solve multiple probabilities… P(1,B) or P(Girls, Boys, 6) Use diagrams to interpret data and probabilities.
(Pg. 178-179)
Compare experimental to theoretical probabilities.
(Pg. 184)