1. Chapter 4 Review MDM 4U
Gary Greer

2. 4.1 Intro to Simulations and Theoretical Probability
be able to design a simulation to investigate the experimental probability of some event
ex: design a simulation to determine the experimental probability of more than one of 5 keyboards chosen in a class will be defective if we know that 25% are defective
get a shuffled deck of cards, choosing clubs to represent the defective keyboards
choose 5 cards and see how many are clubs
repeat a number of times and calculate probability

3. 4.2 Theoretical Probability
work effectively with Venn diagrams
ex: create a Venn diagram illustrating the sets of face cards and red cards
S = 52
red & face = 6
red = 20
face = 6

4. 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)/n(S) = 20/30 = 0.666
66.6%

5. 4.2 Theoretical Probability
ex: calculate the probability of not throwing a four with 3 dice
there are 63 possible outcomes with three dice
only 3 outcomes produce a 4
probability of a 4 is:
3/63
probability of not 4 is:
1- 3/63

6. 4.3 Finding Probability Using Sets
recognize the different types of sets
utilize the additive principle for unions of sets
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)
calculate probabilities using the additive principle

7. 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

8. 4.4 Conditional Probability
calculate a probability of events A and B occurring, given that A has occurred
use the multiplicative law for conditional probability
ex: what is the probability of drawing a jack and a queen in sequence, given no replacement?
4/52 x 4/51

9. 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
a) Draw a Venn Diagram that represents this situation.
b) What is the probability that a student takes Mathematics given that he or she also takes English?

10. 4.4 Conditional ProbabilityE 17 45 1 5 2 5 25

11. 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 /

12. 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

13. 4.5 Tree Diagrams and Outcome Tables
Mr. Greer is going fishing
he finds that he catches fish 70% of the time when the wind is out of the east
he also finds that he catches fish 50% of the time when the wind is out of the west
if there is a 60% chance of a west wind today, what are his chances of having fish for dinner?
we will start by creating a tree diagram

14. 4.5 Tree Diagrams and Outcome Tables
0.5
fish dinner
P=0.3
west
0.6
0.5
bean dinner
P=0.3
fish dinner
0.7
P=0.28
0.4
east
0.3
bean dinner
P=0.12

15. 4.5 Tree Diagrams and Outcome Tables
P(east, catch) = P(east) x P(catch | east)
= 0.4 x 0.7 = 0.28
P(west, catch) = P(west) x P(catch | west)
= 0.6 x 0.5 = 0.30
Probability of a fish dinner: = 0.58
So Mr. Greer has a 58% chance of catching a fish for dinner

16. 4.6 Permutations
find the number of outcomes given a situation where order matters
calculate the probability of an outcome or outcomes in situations where order matters
recognizing how to restrict the calculations when some elements are the same

17. 4.6 Permutations
ex: in a class of 10 people, a teacher must choose 3 for an experiment (students are done in a particular order)
how many ways are there to do this?
ans: P(10,3) = 10!/(10 – 3)! = 720?
ex: how many ways can 5 students be arranged in a line?
ans: 5!
ex: how many ways are there above if Jake must be first?
ans: (5-1)! = 4!

18. 4.6 Permutations
ex: what is the chance of opening one of the school combination locks by chance?
ans: 60 x 60 x 60

19. 4.7 Combinations
find the number of outcomes given a situation where order does not matter
calculate the probability of an outcome or outcomes in situations where order does not matter
ex: how many ways are there to choose a 3 person committee from a class of 20?
ans: C(20,3) = 20!/((20-3)!3!)

20. 4.7 Combinations
ex: from a group of 5 men and 4 women, how many committees of 5 can be formed with
a. exactly 3 women
b. at least 3 women
ans a:
ans b: