Ch 6.3 General Probability Rules
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Transcript of Ch 6.3 General Probability Rules
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 R2000s 2 13 22 21990s 1 1 7 01980s 0 1 0 01970s 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 R2000s 2 13 22 21990s 1 1 7 01980s 0 1 0 01970s 0 1 0 0
6.69, 71, 78
Have a wonderful weekend!
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