1. Probability Rules

3. Monty Hall “Let’s Make a Deal”
Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats.
You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat.
You have the option to stay with your original door choice or to switch to #2. Is it to your advantage to switch?

5. “Let’s Make a Deal”
Make a prediction with your partner about what you think we should do.
Three cards (two of one color= goats, other color= car)
Designate one person to be the game show host (you’ll switch roles eventually)
The host should shuffle and arrange the cards so that only they know where the ‘car’ is.
Contestant then picks a door.
Host reveals one of the doors that wasn’t picked and that has a goat.
Contestant decide one of three things: 1) switch 2) stay 3) flip a coin- H=switch, T=stay
Record data

6. Data Collection Switch 5 times, Stick 5 times, flip my coin 5 times
Trial
Stick/Switch/Coin Flip & Sw or St
Win/Lose 1 2
… 15 trials total per person

7. The host must always open a door that was not picked by the contestant
The host must always open a door to reveal a goat and never the car.
The host must always offer the chance to switch between the originally chosen door and the remaining closed door.

10. An intuitive explanation is that, if the contestant initially picks a goat (2 of 3 doors), the contestant will win the car by switching because the other goat can no longer be picked, whereas if the contestant initially picks the car (1 of 3 doors), the contestant will not win the car by switching

11. Most people come to the conclusion that switching does not matter because there are two unopened doors and one car and that it is a 50/50 choice. This would be true if the host opens a door randomly, but that is not the case; the door opened depends on the player's initial choice, so the assumption of independence does not hold

12. Vocab
Probability Model
Sample Space
Event

13. How could we find S?
Make an exhaustive list.
Use counting principles.
Run a simulation.
Somebody gives it to us! 

14. Let’s consider the following example:
What is the sample space for the genders of a family consisting of exactly three children?
BBB, BBG, BGB, BGG, GGG, GGB, GBG, GBB

15. Toss a Fair Coin
Find the sample space for tossing a fair coin four times.
Find the probability model for # of tails
Find P(0), P(>2)

16. Probability Rules The probability of any event is a # btwn 0 and 1
All possible outcomes together must have probability 1
The prob. That an event does NOT occur is 1- prob that is does occur (complement)
If two events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities.
If all outcomes in the SS are equally likely, the prob that event A occurs can be found using formula:
P(A)= # of outcomes corresp to event A/ Total number of outcomes

17. Tossing 2 Fair 6-sided Dice
Imagine rolling these dice- one that’s red and one that’s green.
What is the sample space?
What is probability of each outcome?
P(rolling a 5)?
P(rolling not a 5)?

18. Marital Status Woman aged 25-29 years old and their marital status
P(Widowed)?
P(Not married)?
Marital Status
Never Married
Married
Widowed
Divorced
Probability
0.506
0.452
0.002
0.04\\\

19. Two-Way Tables Standard deck of cards (no jokers)= 52 cards
A= getting a face card and B= getting a heart
Heart
Not a Heart
Face card
Not a face card

20. P(A)=? P(B)=? P(A and B)=? P(A or B)=? Heart Not a Heart Face card
Not a face card
P(A)=?
P(B)=?
P(A and B)=?
P(A or B)=?

21. Rules Again
P(A or B) = P(A)+P(B)- P(A and B)
P(A and B)= P(A)*P(B\A)

22. Two-Way Tables Yes PE No PE Total Male 19 71 90 Female 84 4 88 103 75
Pierced ears?
A= pierced ears B= is a male
P(A)?
P(A and B)?
P(B and A)?
P(A or B)?
Yes PE
No PE
Total
Male 19 71 90
Female 84 4 88
103 75
178

23. Two-Way Tables
Shuffle a standard deck of playing cards and deal one card. Let event J= getting a jack and event R=getting a red card.
Construct a two-way table that describes the sample space in terms of events J and R
Find P(J), P(R), P(J or R), and P(J and R)

24. Venn Diagram Standard deck of cards (no jokers)= 52 cards
A= getting a face card and B= getting a heart

25. Venn Diagram Yes PE No PE Total Male 19 71 90 Female 84 4 88 103 75
178

26. Vocab
Mutually Exclusive/Disjoint
Getting a Heart
Getting a Black Card

27. Genetics at Work Try to curl their tongue
Interlock the fingers of your hands. Note which thumb (right or left) comes out on top.
Gather data from 12 of your classmates (yourself included). Make sure you keep their data together and label with their initials (e.g., EM yes curl, left on top)
T= can curl tongue and R= right thumb on top

28. Genetics
Make a Venn diagram that shows where each member of your set of data falls with respect to the two events. Use initials to represent each student.
Make a two-way table that summarizes the number of students in each of the four regions of the Venn diagram
Find P(T)
Find P(T and R)
Find P(T or R)
Find P(Tc)
Find P(Tc and Rc)
Challenge: Consider the event F= is female. See if you can construct a Venn diagram with three circles to classify the members of your class with respect to events T, R, and F.