Ch 6.3 General Probability Rules

AP STATISTICS

Theoretical: true mathematical probability Empirical: the relative frequency with which

an event occurs in a given experiment Subjective: an educated guess

Types of Probability

Experiment: any process that yields a result or

observation Outcome: a particular result of an experiment Sample Space: the collection of all possible outcomes Event: any collection of outcomes; any subset of the

sample space Example: Roll die

Let A={1} Let B={2, 4, 6} Let C={3, 6}

An event occurs if any outcome of the event occurs

Review Terms

P(A) = # of outcomes/# outcomes in

sample space If each outcome is equally likely

Using previous slide’s events: P(A)= P(B)= P(C)=

Probability of Event

Rule 1: For any event, Rule 2: Complement Rule

“A complement” is the event that A does not occur; the set of all outcomes not in A

Example: even/odd; alive/dead P(ACE)= P(ACE’)=

Rules of Probability

Rule 3: Mutually Exclusive/disjoint-two events,

A & B that have no outcomes in common Examples: red and spade; freshman,

sophomore, junior Note: complementarymutually exclusive ;

mutually exclusivecomplementary Rule 4: Additive Rule for disjoint events

Example: P(red or spade)=P(red) + P(spade)=

Rules of Probability

Rule 5: Additive Rule-For any events A & B, P(A or B)=P(A)+P(B)-P(A and B)

Example: Find the probability of drawing red card or Ace.

Rule 6: Conditional Probability-For two events A and B, the probability that A occurs given that B has occurred.

Rules of Probability

Example: What is the probability that a card is a

diamond, given that it is red?

Example: What is the probability of 2, given that you got an even number?

Probability Rules

2 events A and B are independent if the occurrence of one

event doesn’t affect the probability of occurrence of the other event

To prove:

Example: rolling two dice; drawing from a deck with replacement

Are drawing a face card and drawing a red card independent events?

So they are independent.

Independent Events

Rule 7: Multiplicative Rule for Independent Events-

Has to be shown or given Example: Find the probability of drawing two

Queens from a deck of cards if it is done with replacement.

Rule 8: Multiplicative Rule- For any two events A& B, the or Example: Find the probability of drawing two

Queens from a deck of cards if it is done without replacement

Probability Rules

G PG PG-13 R

2000s 2 13 22 2

1990s 1 1 7 0

1980s 0 1 0 0

1970s 0 1 0 0

P(1990’s)= P(PG-13)= P(1990s and PG-13)= Are 1990s and PG-13 disjoint events?

Example: Contingency Table

The probability that a randomly selected DVD is

rated PG-13 or is from the 1990s. P(PG-13 or 1990s)=P(PG13)+P(90s)-P(PG13 and 90s)=.58+.18-.14=.62

Are PG-13 and 1990s independent or dependent events?

dependentOther ways:

G PG PG-13 R

2000s 2 13 22 2

1990s 1 1 7 0

1980s 0 1 0 0

1970s 0 1 0 0

6.69, 71, 78

Have a wonderful weekend!

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