AP Statistics – 6.2 Probability Models – Notes
I.
The Idea of Probability a.
Chance behavior is unpredictable in the short term but has a regular pattern in the long run. b.
Probability of an event if the likelihood the event will occur.
II.
The Language of Probability a.
Empirical – based on observation rather than theorizing. b.
Random Phenomenon – if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a larger number of repetitions. c.
Probability – of any outcome of a random phenomenon is the proportion of times the outcome would occur in a very long series of repetitions. That is, probability is long term relative frequency.
(Homework: 6.23, 6.27, 6.28)
III.
Probability Models a.
sample space S – the set of all possible outcomes b.
Event – is any outcome or set of outcomes of a random phenomenon (subset of the sample space). c.
Probability Model – mathematical description of a random phenomenon consisting of two parts: a sample space S and a way of assigning probabilities to events. d.
Sampling with replacement – selecting an individual, putting the individual back into the population, and selecting a second individual e.
Sampling without replacement – selecting an individual, do not replace the individual
IV.
Determining All Outcomes a.
List out the sample space b.
Create a tree diagram c.
Multiplication Rule of Counting – If you can do one task in n1 number of ways and a second task in n2 number of ways, the both takes can be done in n1 x n2 number of ways.
(Homework: 6.29, 6.32, 6.33, 6.35, 6.36)
V.
Probability Rules a.
The probability P A A satisfies 0

P A

1 . b.
If S is the sample space in a probability model, then P(S) = 1 . (Sum of probabilities has to = 1.) c.
If two events are disjoint (mutually exclusive) if they have no outcomes in common (can not occur at the same time). If A and B are disjoint, then P AorB )

P A

P B . This is the addition rule for disjoint events. d.
The complement of any event A is the event that A does not occur written as A
C
. The complement rule states that P A
C
( ) . e.
Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs. If A and B are independent, P AandB )

P A P B . This is the multiplication rule for independent events. f.
If random phenomenon has k possible outcomes that are all equally likely, then each individual outcome has probability
1 k

# outcomesA

# outcomesS
. The probability of any event A is
# outcomesA k

Disjoint Events Complements
Not Disjoint Events
VI.
Notation a.
A


B b.
A B
(“A union B”) – A OR B
( “A intersect B”) – A AND B c.

- empty event
C d.
e.
A
A
- Complement of A – Not A
B (“A intersect B” is empty”) – disjoint (mutually exclusive) events
(Homework: 6.37-6.40, 6.44 )
Independent Events:
(Homework: 6.45-6.52)