HW- pgs. 423-425 (6.37-6.41, 6.43-6.44)
6.1 & 6.2 Take home Quiz Due FRIDAY 11-22-13
Ch. 6 Test TUESDAY 12-3-13
www.westex.org HS, Teacher Website
11-20-13
Warm up—AP Stats
When selecting one card, what is the probability of
drawing:
1. a heart or a club?
2. a heart or a 3?
3. a heart and a club?
3. a heart and a 3?
Name _________________________
AP Stats
6 Probability and Simulation: The Study of Randomness
6.2 Probability Models Day 3
Date _______
Objectives
 List the four rules that must be true for any assignment of probabilities.
 Explain what is meant by {A U B} and {A ∩ B}.
 Give an example of two events A and B where A ∩ B = Ø.
 Explain what is meant by equally likely outcomes.
Probability Rules
Thinking of probability as “the __________-__________ proportion of repetitions on which
an event occurs” four facts follow:
1. Any probability is a number between 0 and 1.
2. The sum of the probabilities of all possible outcomes must equal 1. (some outcome
MUST occur on every trial.)
3. If two events have NO OUTCOMES IN COMMON, the probability that one or the
other occurs is the sum of their individual probabilities. Ex. Deck of cards:
4. The probability that an event does not occur is 1 minus the probability that the
event does occur.
Probability Rules in Formal Language
1.
2.
3.
4.
We can use set notation to describe events. The event A U B is read “A _______ B” and is
the SET of all outcomes that are either in A OR in B. U means union/or. ∩ means
intersect/and. The symbol Ø means empty set. If two events A and B are disjoint (mutually
exclusive) we can write A ∩ B = Ø and it’s read “A intersect B is empty.” Ex. If A is the
event of drawing a heart in a standard deck of cards and B is the event of drawing a
spade in a standard deck of cards, then P(A ∩ B) = Ø because a card can’t be both a
heart and a spade at the same time. Events A and B are disjoint/mutually exclusive!
Look at the text below and Figures 6.3 and 6.4 to learn about _______ diagrams.
Probabilities in a Finite Sample Space
The probability of any event is the ______ of the probabilities of the outcomes making up the
event. See example 6.15 below to see sums of probabilities in action!
(b) Find the probability that the first digit is anything other than a 1.
(c) What is the probability that the first digit is a 1 or is a 6 or greater? (write it out
symbolically and solve)
(d) Event C is that the first digit is odd. What is the probability of event C?
(e) What is the probability of event B or event C occurring?
Equally Likely Outcomes
A coin is considered ____________ likely to land heads or tails. A number picked from a
Random digit table is considered to be equally likely to be any digit from 0-9. See example
6.16 below.
If we randomly select 3 numbers from 1 to 3 what proportion of the time will at least 1 digit
occurs in its correct position? For example, in the number 213 one digit (the 3) was in its
correct position.
Use your calculator to randomly generate a three-digit number. Do 20 trials and use the table
below (tally marks) to record your results. We will then pool our results together and see
what proportion of the time at least one digit occurred in its correct position.
At least one digit in the correct position
NOT
6.42 Determine the theoretical probability that at least one digit will occur in its correct
position.
b) Compare the theoretical probability with our results (empirical) from our simulation.