Download AP Stat Ch. 6 Day 3 Lesson Worksheet 08

AP STATISTICS
Chapter 6 – Probability: The Study of Randomness
Section 6.2: Probability Models
Name _______________________
Date __________
Period _____
Day 3 Assignment: 6.34-6.38, 6.40, 6.41, 6.44, 6.45
A. Key Vocabulary: random phenomenon, probability, probability model, sample space S,
set of outcomes, events, P(A) – probability of event A, complement - Ac, disjoint events,
independence of events, independent, basic properties of probability, tree diagram, multiplication principle,
with replacement, without replacement, union, intersection, empty event, Venn diagram, finite sample
space, infinite sample space, equally likely outcomes, ,,
B. Review Day 2 Assignment: Exercises 6.12, 6.14, 6.18, 6.20, 6.22, 6.26
C. Probability Models - key ideas:
The sample space S of a random phenomenon is the set of all possible outcomes.
Roll a die:
S = {1,2,3,4,5,6}
An event is any outcome or set of outcomes of a random phenomenon. That is, an event is a subset
of the sample space.
Let A be the event “roll an even”:
A = {2,4,6}
A probability model is a mathematical description of a random phenomenon consisting of two
parts: a sample space S and a way of assigning probabilities to events.
D. What is the sample space for rolling two dice and counting the pips?
E. Multiplication principle (for counting): If you can do one task in a ways and a second task in b ways,
then both can be done in a x b ways.
Roll a die, flip a coin, pick a random digit. How many outcomes are possible?
How many boy/girl pairs are possible in this class?
F. With and without replacement illustrated:
How many 4 digit numbers starting with 5 are possible?
How many 4 digit numbers starting with 5 are possible if digits can’t be used again?
G. Probability Rules:
Rule 1. The probability P(A) or any event A satisfies 0  P( A)  1 . (Any probability is a number
between 0 and 1.)
Rule 2. If S is the sample space in a probability model then P(S) = 1. (All possible outcomes together
must have a probability 1.)
Rule 3. The complement of any event A is the event that A does not occur, written as Ac. The complement
rule states that:
P(Ac) = 1 – P(A)
(The probability that an event does not occur is 1 minus the probability that the event does occur.)
Rule 4. Two events A and B are disjoint (also called mutually exclusive) if they have no outcomes in
common (do not intersect) and so can never occur simultaneously. If A and B are disjoint, then:
P(A or B) = P(A) + P(B)
(If two events have no outcomes in common, the probability that one or the other occurs is the sum of
their individual probabilities.)
Rule 5. If A and B are not disjoint, then
P(A or B) = P(A) + P(B) – P(A and B)
Rule 6. 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, then:
P(A and B) = P(A)P(B)
This is the multiplication rule for independent events.
We use this rule as a matter of course all the time. Example – toss coin and die. P(H3) = ?
H. Disjoint events and independence: disjoint events are not independent!
Exercise 6.45: Assume events A and B are non-empty, independent events
Prove that A and B must intersect (i.e., are not disjoint)
I. Example 6.14 Atlantic Telephone Cable (p. 353)
J. Example 6.15 AIDS Testing (p. 354)