Transcript PROBABILITY RULES

PROBABILITY RULES
Chapters 14/15
AP Statistics
Mrs. Wolfe
What is probability?
• Probability is the long run relative frequency
of some occurrence
Probability of event A = P(A)
P(A)= number of successful outcomes
number of total outcomes
Example 1:
Imagine that a bowl contains the following
Marbles: 4 green, 2 blue, 3 white, 1 red.
P(Green) = ?
P(Red or blue)= ?
P(not white) = ?
P (green and blue)= ?
Important words in Probability
OR—means to add
also means the UNION(U) of sets A and B
P(A U B) = P(A) + P(B)- P(A∩ B)
2nd Important Word
AND--means to multiply
also means the INTERSECTION (∩)
of sets A and B
P(A ∩ B) = P(A) ∙ P(B)
assumes A and B are INDEPENDENT
3rd Important Word
NOT—means to subtract from 1 or from 100%
A c or Ā or A’=the complement of A
c
P(A )
= 1 – P(A)
KEY VOCABULARY
Trial—a single attempt of a random occurrence
Outcome—the value measured or observed for
an individual trial
Event—a collection of outcomes-designated
with capital letters A, B, C, etc.
Sample Space—collection of all outcomes possible
TYPES OF PROBABILITY
Theoretical—mathematical computation
involved to determine what should happen
Empirical—experiment performed to count
chance of event happening
Subjective—educated guess –no real
probability theory used
LAW OF LARGE NUMBERS
In the long run, empirical probability will settle
down toward the theoretical probability.
Does not mean that the “Law of Averages” will
be true…just because a coin hasn’t been
heads in 5 tries, it still has a 50% chance
of being heads on the next try!
PROPERTIES OF PROBABILITY
1. Probability of all outcomes must
sum to 1.
2. 0 < P(x) < 1
EXAMPLE USING VENN DIAGRAMS
Police reports that 78% of drivers stopped on
suspicion of drunk driving are given a breath
test, 36% a blood test and 22% are given both
tests. What is the probability of
a. a test?
b. a blood test or a breath test, but not both?
c. neither test?
Important Event Concepts
Disjoint Events—also called mutually exclusive
means that A and B share no common
outcomes
Independent Events—how one event occurs
does not affect the probability of the
second event
Independent? Mutually exclusive?
Given P(A) = 0.6 and P(B) = 0.3.
P (A U B) = 0.75. Are A and B mutually
exclusive?
P(A ∩ B) = 0.18. Are A and B
independent?
Blood type problem
45% type O, 40% type A, 11% type B, 4%
type AB
What is the probability of a person being
Type A and Type O?
What is the probability of two persons in a
row being Type A?
Car Problem Review
Suppose 40% of cars in your area are
manufactured in the US, 30% in Japan, 10% in
Germany and 20% in other countries.
If a car is selected at random, find
a. P(car not US made)
b. P(car from Japan or Germany)
c. P(two cars in a row from Japan)
d. P(at least one of three cars is US made)
CONDITIONAL PROBABILITY-CHART
Public
Private
Total
Male
180
110
290
Female
95
55
150
Totals
275
165
440