1. Unit 1 Review MDM 4U
Chapters 4.1 – 4.5

2. Test Format 20 MC K/U (answer 4 of 4) APP (answer 4 of 6)
TIPS (answer 2 of 3)
COMM (15% - using formulas, good form, rounding, concluding statements)

3. Steps to Solving Probability Problems
G = Given: List knowns, draw diagram / table / list
R = Required to find: Identify the unknown, look for keywords
A = Analyze: Write the formula or explain your thinking
S = Solve: Plug knowns into formula and/or compute
P = Present: State your answer using a sentence

4. U1 Learning Goals
Calculate experimental probability given the results of an experiment
Design a simulation for a given scenario
Calculate the theoretical probability for simple or compound events
Recognize and calculate conditional probability
Weather, pro athletes, timed traffic signals, dealing cards
Recognize and calculate intersection based on a conditional probability (dealing cards)
Use the multiplicative principle for union (or intersection)
Create or use a Venn diagram to calculate probability
Construct a tree diagram or outcome table and use it to calculate probability

5. 4.1 Intro to Simulations and Experimental Probability
Design a simulation to model the probability of an event
Ex: design a simulation to determine the experimental probability that more than one of 5 keyboards chosen in a class will be defective if we know that 25% are defective
1. Get a well-shuffled deck of cards, choosing clubs to represent a defective keyboard
2. Choose 5 cards with replacement and record how many are clubs
3. Repeat a large number of times and calculate the experimental probability

6. 4.2 Theoretical Probability
Calculate the probability of an event or its complement
Ex: What is the probability of randomly choosing a male from a class of 30 students if 10 are female?
P(A) = n(A) = 20 = n(S) 30

7. 4.2 Theoretical Probability
Ex: Calculate the probability of not throwing a total of four with 3 dice
There are 63 = 216 possible outcomes with three dice
Only 3 outcomes produce a 4
P(sum = 4) = 3_
216
probability of not throwing a sum of 4 is:
1 – = 213 = 0.986

8. 4.3 Finding Probability Using Sets
Recognize the different types of sets (union, intersection, complement)
Utilize:
The Additive Principle for the Union of Two Sets:
n(A U B) = n(A) + n(B) – n(A ∩ B)
P(A U B) = P(A) + P(B) – P(A ∩ B)
The Additive Principle for the Intersection of Two Sets:
n(A ∩ B) = n(A) + n(B) – n(A U B)
P(A ∩ B) = P(A) + P(B) – P(A U B)

9. 4.3 Finding Probability Using Sets
Work with Venn diagrams
ex: Create a Venn diagram illustrating the sets of face cards and red cards
red & face = 6
face = 6
red = 20
S = 52

10. 4.3 Finding Probability Using Sets
Ex: What is the probability of drawing a red card or a face card
Ans: P(A U B) = P(A) + P(B) – P(A ∩ B)
P(red or face) = P(red) + P(face) – P(red and face)
= 26/ /52 – 6/52
= 32/52
= 0.615

11. 4.3 Finding Probability Using Sets
What is n(B υ C)
= 34
What is P(A∩B∩C)?
n(A∩B∩C) = 3 = 0.07
n(S) 43

12. 4.4 Conditional Probability
100 Students surveyed
Course Taken
No. of students
English 80
Mathematics 33
French 68
English and Mathematics 30
French and Mathematics 6
English and French 50
All three courses 5
What is the probability that a student takes Mathematics given that he or she also takes English?

13. 4.4 Conditional ProbabilityE
4.4 Conditional Probability 17 45 1 5 2 5 25

14. 4.4 Conditional Probability
To answer the question in (b), we need to find P(Math|English).
We know...
P(Math|English) = P(Math ∩ English)
P(English)
Therefore…
P(Math|English) = 30 / 100 = 30 x = 3
80 /

15. 4.4 Conditional Probability
Calculate the probability of event B occurring, given that A has occurred
Need P(B|A) and P(A)
Use the multiplicative law for conditional probability
Ex: What is the probability of drawing a jack and a queen in sequence, given no replacement?
P(1J ∩ 2Q) = P(2Q | 1J) x P(1J)
= 4 x 4 = = 0.006

16. 4.5 Tree Diagrams and Outcome Tables
A sock drawer has a red, a green and a blue sock
You pull out one sock, replace it and pull another out
Draw a tree diagram representing the possible outcomes
What is the probability of drawing 2 red socks?
These are independent events R B G

17. 4.5 Tree Diagrams and Outcome Tables
Mr. Lieff is playing Texas Hold’Em
He finds that he wins 70% of the pots when he does not bluff
He also finds that he wins 50% of the pots when he does bluff
If there is a 60% chance that Mr. Lieff will bluff on his next hand, what are his chances of winning the pot?
We will start by creating a tree diagram

18. Tree Diagram 0.5 Win pot P=0.6 x 0.5 = 0.3 bluff 0.6 0.5 Lose pot
0.7
0.4
P=0.4 x 0.7 = 0.28
no bluff
0.3
Lose pot
P=0.4 x 0.3 = 0.12

19. 4.5 Tree Diagrams and Outcome Tables
P(no bluff, win) = P(no bluff) x P(win | no bluff)
= 0.4 x 0.7 = 0.28
P(bluff, win) = P(bluff) x P(win | bluff)
= 0.6 x 0.5 = 0.30
Probability of a win: = 0.58
So Mr. Lieff has a 58% chance of winning the next pot

20. Continued… P(no bluff, win) = P(no bluff) x P(win | no bluff)
P(bluff, win) = P(bluff) x P(win | bluff)
= 0.6 x 0.5 = 0.30
Probability of a win: = 0.58
So Mr. Lieff has a 58% chance of winning the next pot

21. Review Read class notes and home learning Complete
pp #3-4, 5abceg, 7, 9, 10
p. 270 #1-2, 6
Practice Test on web site