ap statistics, section 6.3, part 1

Warm Up Chapter 6.2 Quiz Today

1. 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.

2. Redo #1 but this time return the card.

AP Statistics, Section 6.3, Part 1 2

Section 6.3.1Probability Models

AP Statistics

4

Venn Diagrams: Disjoint Events

AB

S

S = (sample space=all possible outcomes.)

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.

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”. 5


Venn Diagrams: Disjoint Events

AB

S

( or ) ( ) ( )P A B P A P B


Venn Diagrams: Non-disjoint Events

A

B

S

( or ) ( ) ( ) ( and )P A B P A P B P A B

A and B


Venn Diagrams: Non-disjoint Events

A

B

S

( ) ( ) ( ) ( )P A B P A P B P A B

A and B


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.


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


Example

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

.5.7

D and M

.3.4 .2

.1


Example

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

.2.4

D and M

.3

.1


Different Look

Matthew

Promoted Not Promoted Total

DeborahPromoted .3 .7

Not Promoted

Total .5


Different Look

Matthew


DeborahPromoted .3 .7

Not Promoted

Total .5 1.0


Different Look

Matthew


DeborahPromoted .3 .4 .7

Not Promoted .2

Total .5 1.0


Different Look

Matthew



Not Promoted .2 .3

Total .5 .5 1.0


Different Look

Matthew



Not Promoted .2 .1 .3

Total .5 .5 1.0

3 Events Preference in Pizza Toppings for kids.

25% like pepperoni 20% like combination 30% like cheese

Also 10% like both pepperoni and

cheese5% like all three12% like both combination

and cheese 10% like pepperoni only


Whole circle needs to add up to 25%



Adds up to

10%


25% like pepperoni 20% like combination 30%like cheese

Also 10% like both pepperoni and

cheese5% like all three12% like both combination

and cheese 10% like pepperoni only


5%5% 5%

7%

52%

Sample Space Must Add Up to 100%


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%


5%5% 5%

7%

52%

Using a Venn DiagramThe probability of event A

happening is .64The Probability of event B

happening is .20The 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


.12

.28

=.12

=.52

=.08

=.28


Assignment

Exercises: 6.46-6.53, all

ap statistics, section 6.3, part 1

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