Download Chapter 15 Probability Rules! - yobrienmath

Chapter 15
Probability Rules!
General Addition Rule
Conditional Probability
Recall…
• for any Random phenomenon
• each trial generates
• an outcome
• An event is a set of outcomes
– The collection of all possible outcomes is called
the SAMPLE SPACE (S)
Sample Space
List the sample space and tell whether you think
they are equally as likely
a. Toss 2 coins; record the order of heads and
tails
b. A family has 3 children; record the number of
boys
c. Flip a coin until you get a head or 3
consecutive tails
d. Roll two dice; record the larger number
Drawing Venn Diagrams
Real Estate ads suggest that 64% of homes for
sale have garages, 21% have swimming pools,
and 17% have both features. What is the
probability that a home for sale has
a. a pool or a garage?
b. neither a pool nor a garage?
c. a pool but no garage?
General Addition Rule
• Does NOT require disjoint events
P(AÈB) = P(A)+ P(B)- P(AÇB)
Conditional Probabilities
A Gallup survey of June 2004 asked 1005 U.S. adults who they think better
fits their idea of what a first lady should be, Laura Bush or Hillary Clinton.
a.
b.
c.
d.
What is the probability that the person thought Laura Bush best fits
their first lady ideals?
What is the probability that the person is younger than 50?
What is the probability that the person is younger than 50 and thinks
Clinton is a better fit?
What is the probability that the person is younger than 50 or thinks
Clinton is a better fit?
18-29
30-49
50-64
over 65
total
Clinton
135
158
79
65
437
Bush
77
237
112
92
518
Neither
5
21
14
10
50
Total
217
416
205
167
1005
Conditional Probability
“The probability of B given A”
P(A Ç B)
P(B | A) =
P(A)
Conditional Probabilities
You draw a card at random from a standard deck
of 52 cards. Find the following conditional
probabilities.
a. the card is a heart, given that it is red.
b. the card is red, given that it is a heart
c. the card is an ace, given that it is red
d. the card is a queen given that it is a face card
Chapter 15
Probability Rules!
*General Multiplication Rule
*Testing for Disjoint/Independence
*Probability Tables
*Tree Diagrams
General Multiplication Rule
** when A and B are INDEPENDENT, then
P ( AÇ B) = P(A)´ P(B) **
• When A and B are NOT independent, then
P(A Ç B) = P(A) ´ P(B | A)
or
P(A Ç B) = P(B) ´ P(A | B)
Which event you
define as A or B
does not matter
How do we know if two event are
INDEPENDENT??
If P(B|A) = P(B), then A and B are independent
Example: Is good grades as a goal independent
of gender??
Goals
Gender
Grades
Popular
Sports
Total
Boy
117
50
60
227
Girl
130
91
30
251
Total
247
141
90
478
• Events can NOT be disjoint AND independent
• Consider
– Event A = {making the team}
– Event B = {not making the team}
Probability Tables
Construct a probability table with the given
information.
Suppose 78% of DUI suspects are given a breath
test, 36% a blood test, and 22% of DUI suspects
receive both tests.
• Are giving a DUI suspect a blood test and a
breath test mutually exclusive (disjoint)?
• Are giving the 2 tests independent?
Drawing without Replacing
• Suppose you are drawing cards from a
standard deck.
• What is the probability you will draw 3 spades
in a row??
Data on College Binge Drinking
• 44% binge drink
• 37% drink moderately
• 19% abstain completely
• Of those who binge drink: 17% car accidents
• Of those who drink moderately: 9% car
accidents
FIND: P(college student who binge drinks and
has been involved in a car accident)
Tree Diagram
• shows sequence of events
• make when using GMR
• covers all possible outcomes
• probabilities should add up to 1
Reversing the Conditions
• What is the probability the student is a binge
drinking given they were in an accident.
• Tree Diagram given P(accident|binge drinker)
• Use the tree to find P(binge|accident)