1. AP Statistics, Section 6.3, Part 1
Warm Up
Chapter 6.2 Quiz Today
What is the probability of getting an A, with out returning it, and the second card a King from? Assume the deck has 52 cards.
Redo #1 but this time return the card.
I have $100 for a student in this class. What is the probability that you will be selected to win $100 ?
What is the probability that two different females will be selected to win $100 each.
AP Statistics, Section 6.3, Part 1

2. AP Statistics, Section 6.3, Part 1
Warm Up
Chapter 6.2 Quiz Today
What is the probability of choosing an Ace, with out returning it, and then a King from a deck of cards? Assume the deck has 52 cards.
Redo #1 but this time return the card.
AP Statistics, Section 6.3, Part 1

3. Section 6.3.1 Probability Models
AP Statistics

4. Venn Diagrams: Disjoint Events
Not the same as Independent: Independent events must be able to occur at the same time. If one happens, it has no influence on the other whatsoever. The occurrence of one provides no information about the other. S A B
S = (sample space=all possible outcomes.)

5. Independent vs Disjoint
The occurrence of one provides no information about the other.
Ex: You place a bet on a card being red.
I peak and tell you it’s an ace. Does that help you? Before you knew this, the probability the card is red was 26/52 = 1/2. Knowing it’s an ace, the probability it’s red is 2/4 = 1/2. No help whatsoever – the probability has not changed. These two events ARE independent (and not disjoint). P(red | ace) = P(red) — that’s the very definition of independence: the occurrence of “ace” has no effect on the probability of “red”.

6. Venn Diagrams: Disjoint EventsB
AP Statistics, Section 6.3, Part 1

7. Venn Diagrams: Non-disjoint EventsB A
A and B
AP Statistics, Section 6.3, Part 1

8. Venn Diagrams: Non-disjoint EventsB A
A and B
AP Statistics, Section 6.3, Part 1

9. AP Statistics, Section 6.3, Part 1
Example
Deborah and Matthew are awaiting the decision about a promotion. Deborah guesses her probability of her getting a promotion at .7 and Matthew’s probability at .5.
AP Statistics, Section 6.3, Part 1

10. AP Statistics, Section 6.3, Part 1
Example
Deborah and Matthew are awaiting the decision about a promotion. Deborah guesses her probability of her getting a promotion at .7 and Matthew’s probability at .5. D M .5 .7
AP Statistics, Section 6.3, Part 1

11. AP Statistics, Section 6.3, Part 1
Example .1
Since there is not enough information to do the problem, let’s add information. Deborah thinks the probability of both getting promoted is .3 D M
D and M .3 .2 .5 .4 .7
AP Statistics, Section 6.3, Part 1

12. AP Statistics, Section 6.3, Part 1
Example .1
What’s the probability of only Deborah getting promoted P(D-M)?
P(M-D)?
P(Dc)?
P(Mc)?
P(Dc and Mc)? D M
D and M .3 .2 .4
AP Statistics, Section 6.3, Part 1

13. AP Statistics, Section 6.3, Part 1
Different Look
Matthew
Promoted
Not Promoted
Total
Deborah .3 .7 .5
AP Statistics, Section 6.3, Part 1

14. AP Statistics, Section 6.3, Part 1
Different Look
Matthew
Promoted
Not Promoted
Total
Deborah .3 .7 .5
1.0
AP Statistics, Section 6.3, Part 1

15. AP Statistics, Section 6.3, Part 1
Different Look
Matthew
Promoted
Not Promoted
Total
Deborah .3 .4 .7 .2 .5
1.0
AP Statistics, Section 6.3, Part 1

16. AP Statistics, Section 6.3, Part 1
Different Look
Matthew
Promoted
Not Promoted
Total
Deborah .3 .4 .7 .2 .5
1.0
AP Statistics, Section 6.3, Part 1

17. AP Statistics, Section 6.3, Part 1
Different Look
Matthew
Promoted
Not Promoted
Total
Deborah .3 .4 .7 .2 .1 .5
1.0
AP Statistics, Section 6.3, Part 1

18. 3 Events Preference in Pizza Toppings for kids.
Whole circle needs to add up to 25%
3 Events Preference in Pizza Toppings for kids.
25% like pepperoni
20% like combination
30% like cheese
Also
10% like both pepperoni and cheese
5% like all three
12% like both combination and cheese
10% like pepperoni only
Pepperoni
Cheese
Combination
Adds up to 10%
Whole circle needs to add up to 20%
Whole circle needs to add up to 30%
AP Statistics, Section 6.3, Part 1

19. 3 Events Preference in Pizza Toppings for kids.
Pepperoni %
Cheese 13%
Combination 3%
25% like pepperoni
20% like combination
30%like cheese
Also
10% like both pepperoni and cheese
5% like all three
12% like both combination and cheese
10% like pepperoni only
52%
Sample Space Must Add Up to 100% 5% 5% 5% 7%
AP Statistics, Section 6.3, Part 1

20. 3 Events Preference in Pizza Toppings for kids.
Pepperoni %
Cheese 13%
Combination 3%
What percent of kids like only Combination? 3%
What percent kids like none of the three?
52%
What percent like Cheese but not combination?
18%
52% 5% 5% 5% 7%
AP Statistics, Section 6.3, Part 1

21. AP Statistics, Section 6.3, Part 1
Using a Venn Diagram
The probability of event A happening is .64
The Probability of event B happening is .20
The probability of both events occurring is .12.
What is the probability of each event.
A and B
A and Bᶜ
Aᶜ and B
Aᶜ and Bᶜ
A .52 B
.28
.12
=.12
=.52
=.08
AP Statistics, Section 6.3, Part 1
=.28

22. AP Statistics, Section 6.3, Part 1
Assignment
Exercises: , all
AP Statistics, Section 6.3, Part 1