Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Honors Statistics
Aug 23-8:26 PM
1. Welcome to class
2. Please find folder and take
your seat.
3. Notes Quiz 5.3
4. Review Homework C5#6
5. Introduce the concept of INDEPENDENCE
6. Post SLO review
7. Collect folders
Aug 23-8:31 PM
1
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Nov 20-7:56 AM
Honors Statistics
Notes Quiz
Chapter 5 Section 3
Nov 1-1:41 PM
2
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Apr 9-2:22 PM
Nov 9-5:30 PM
3
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Nov 9-5:34 PM
Worksheets ??
How do you want it - the crystal mumbo-jumbo
or statistical probability?
Apr 25-10:55 AM
4
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Dec 14-8:40 AM
0.28
0.14
16
0.276
58
T
P(H ∩ T) = 0
Dec 14-8:40 AM
5
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Dec 4-8:44 AM
73
73
166
86
166
10
38
18
166
18
56
128
166
9
73
9
30
41
166
12
41
18
52
5
166
30
30
42
125
10
41
10
166
10
38
9
30
Dec 4-8:44 AM
6
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Nov 15-10:41 PM
Nov 15-10:41 PM
7
Chapter 5 Section 3 day 2 2016s Notes.notebook
Conditional Probability =
April 18, 2016
P(both events occur)
P(given event occurs)
Nov 15-10:42 PM
May 3-6:12 PM
8
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
At the gym Suppose that 10% of adults belong to health clubs, and 40% of these
health club members go to the club at least twice a week. What percent of all
adults go to a health club at least twice a week? Write the information given in
terms of probabilities, and use the general multiplication rule.
Nov 19-3:11 PM
Testing the test Are false positives too common in some medical tests? Researchers
conducted an experiment involving 250 patients with a medical condition and 750 other
patients who did not have the medical condition. The medical technicians who were
reading the test results were unaware that they were subjects in an experiment.
(a) Technicians correctly identified 240 of the 250 patients with the condition. They also
identified 50 of the healthy patients as having the condition. What were the false positive
and false negative rates for the test?
D=disease
D
T=test result
DC
T+
T-
(b) Given that a patient got a positive test result, what is the probability that the patient
actually had the medical condition? Show your work.
Nov 19-3:29 PM
9
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Dec 3-9:50 AM
Nov 15-10:43 PM
10
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Aug 22-3:36 PM
NO Association
equals
INDEPENDENT
EVENTS
Aug 24-9:35 PM
11
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
(This table is based closely on grade distributions at an actual university, simplified a bit for clarity.)11
3392
2952
3656
6300
1600
2100
10000
College grades tend to be lower in engineering and the physical sciences (EPS)
than in liberal arts and social sciences (which includes Health and Human
Services). Choose a University of New Harmony course grade at random.
Consider the two events E: the grade comes from an EPS course,
and L: the grade is lower than a B.
1. Find P(L). Interpret this probability in context.
2. Find P(E | L) and P(L | E).
3. Which of these conditional probabilities tells you whether
this college’s EPS students tend to earn lower grades than
students in liberal arts and social sciences? Explain.
The P(L E) gives the probability that a student gets grades
lower than B's if they are Engineering students. Because the
P(L E) = 0.50 which is higher than just P(L) = 0.3656 this tells
us that compared to the rest of the college, engineering
students tend to get lower grades more often than nonengineering students. (Well duh ... their classes do tend to be
harder with more challenging material).
Nov 15-11:02 PM
Are getting low grades and having an
EPS major Independent events at
the University of New Harmony?
Obviously Not and here is why ...
Does P(L E) = P(L)
Does P(E L) = P(E)
OR
DOES P(E) P(L) = P(E ∩ L)
Dec 2-8:26 PM
12
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Nov 14-6:49 PM
.3
≠ .18
OR
Does P(A) = P(A I B) ???
0.2
Does 0.6 = ------- = 0.666 NO
0.3
.1
P(B) = P(B I A) ??
0.3
0.4 = ------- = 0.375 NO
0.8
Nov 19-9:47 AM
13
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
∩
P(A) = P(A l B)
P(B) = P(B l A)
Dec 5-2:31 PM
Nov 15-10:59 PM
14
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Nov 15-11:09 PM
Let L = passenger has a laptop, Let L = passenger has no laptop
Let S = passenger is searched, Let S
Dec 2-9:04 PM
15
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Aug 23-4:18 PM
Apr 18-8:53 AM
16
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Apr 18-8:56 AM
How do you want it - the crystal mumbo-jumbo
or statistical probability?
Contest winners only do the ODD #'s
Apr 25-10:55 AM
17
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Get rich A survey of 4826 randomly selected young adults (aged 19 to 25) asked, “What
do you think are the chances you will have much more than a middle-class income at age
30?” The two-way table shows the responses.16 Choose a survey respondent at random.
(a) Given that the person selected is male, what’s the probability that he answered
“almost certain”?
597
P(AC I M) = --------- = 0.2428
2459
(b) If the person selected said “some chance but probably not,” what’s the probability
that the person is female?
426
P(F I ScPn) = --------- = 0.5983
712
Nov 18-8:16 PM
319
261
627
442
765
1207
A Titanic disaster In 1912 the luxury liner Titanic, on its first voyage
across the Atlantic, struck an iceberg and sank. Some passengers got off
the ship in lifeboats, but many died. The two-way table gives
information about adult passengers who lived and who died, by class of
travel. Suppose we choose an adult passenger at random.
> (a) Given that the person selected was in first class, what’s the probability that he or she survived?
197
P(Survived I FC) = --------- = 0.6176
319
> (b) If the person selected survived, what’s the probability that he or she was a third-class passenger?
151
P( third class I Survived) = --------- = 0.3416
442
Nov 18-8:17 PM
18
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
60
40
83
17
100
Sampling senators The two-way table describes the members of
the U.S. Senate in a recent year. Suppose we select a senator at
random. Consider events D: is a democrat, and F: is female.
(a) Find P(D | F). Explain what this value means.
13
P(D I F) = --------- = 0.765
17
What is the probability that you are a democrat
given that you are a female senator? 76.5%
(b) Find P(F | D). Explain what this value means.
13
P(F I D) = --------- = 0.217 What is the probability that you are a female
given that you are a democratic senator? 76.5%
60
ARE THESE EVENT INDEPENDENT?
ARE GENDER AND PARTY Independent events for the U.S. Senators?
Nov 18-8:19 PM
Who eats breakfast? The following two-way table describes the 595 students who
responded to a school survey about eating breakfast. Suppose we select a student at
random. Consider events B: eats breakfast regularly, and M: is male.
(a) Find P(B | M). Explain what this value means.
190
P(B I M) = --------- = 0.5938
320
What is the probability that you are a male
given that you eat breakfast regularly 59.38%
(b) Find P(M | B). Explain what this value means.
190
P(M I B) = --------- = 0.6333
300
What is the probability that you eat breakfast
regularly given that you are a male? 63.33%
ARE THESE EVENT INDEPENDENT?
ARE GENDER AND Breakfast habits Independent events?
Nov 18-8:19 PM
19
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Foreign-language study Choose a student in grades 9 to 12 at
random and ask if he or she is studying a language other than
English. Here is the distribution of results:
> (a) What’s the probability that the student is studying a language other than English?
P(other than English) = 1 = P(none) = 1 - 0.59 = 0.41
> (b) What is the conditional probability that a student is studying Spanish given that he or she is
studying some language other than English?
0.26
P( S I other than English) = -------- = 0.6341
0.41
Nov 18-8:20 PM
Income tax returns Here is the distribution of the adjusted gross income (in
thousands of dollars) reported on individual federal income tax returns in a
recent year:
> (a) What is the probability that a randomly chosen return shows an adjusted gross income
of $50,000 or more?
P(income ≥ 50000) = 0.215 + 0.100 + 0.006 = 0.321
> (b) Given that a return shows an income of at least $50,000, what is the conditional
probability that the income is at least $100,000?
0.106
P( income ≥ 100,000 I income ≥ 50,000) = ----------- = 0.3302
0.321
Nov 18-8:21 PM
20
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Tall people and basketball players Select an adult at random.
Define events T: person is over 6 feet tall, and B: person is a
professional basketball player. Rank the following
probabilities from smallest to largest. Justify your answer.
P(T)
P(B)
P(T | B)
P(B | T)
P(B) ... some people play basketball (few pro)
P(B I T) ... some tall people play basketball
P(T)... more of the population of adults are tall
P(T I B) ... almost all pro basketball players are tall
Nov 18-8:22 PM
Teachers and college degrees Select an adult at random. Define events A: person
has earned a college degree, and T: person’s career is teaching. Rank the following
probabilities from smallest to largest. Justify your answer.
P(A)
P(T)
P(A | T)
P(T | A)
P(T)... some of the population of adults are teachers
P(T I A) ... some people who have college degrees are teachers
P(A) ... many people have college degrees
P(A I T) ... all teachers have college degrees
Nov 18-8:29 PM
21
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Facebook versus YouTube A recent survey suggests that 85% of college students have
posted a profile on Facebook, 73% use YouTube regularly, and 66% do both. Suppose we
select a college student at random and learn that the student has a profile on Facebook.
Find the probability that the student uses YouTube regularly. Show your work.
FACE
NF
UTube 0.66
0.07
0.73
0.19
0.08
0.27
0.85
0.15
NU
1.00
0.66 = 0.7765
P( UTube I Face) = ---------0.85
Nov 18-8:22 PM
Mac or PC? A recent census at a major university revealed that 40% of
its students mainly used Macintosh computers (Macs). The rest mainly
used PCs. At the time of the census, 67% of the school’s students were
undergraduates. The rest were graduate students. In the census, 23% of
the respondents were graduate students who said that they used PCs as
their primary computers. Suppose we select a student at random from
among those who were part of the census and learn that the student
mainly uses a PC. Find the probability that this person is a graduate
student. Show your work.
MAC
PC
0.30
0.37
0.67
Grad 0.10
0.23
0.33
0.40
0.60
1.00
Und
0.23 = 0.383
P(G I PC) = ---------0.60
Nov 18-8:23 PM
22
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Free downloads? Illegal music downloading has become a big problem: 29% of
Internet users download music files, and 67% of downloaders say they don’t care if
the music is copyrighted.17 What percent of Internet users download music and don’t
care if it’s copyrighted? Write the information given in terms of probabilities, and use
the general multiplication rule.
P( IDK and download)
P( IDK I download) = ----------------P(download)
x
0.67 = ---------0.29
x = (0.67)(0.29)
x = 0.1943
P( IDK and download) = 0.1943 or 19.4%
Nov 18-8:23 PM
Coffee
Tea
Cola
Nov 20-7:20 AM
23
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
B
A
C
Nov 20-7:20 AM
Nov 22-10:19 PM
24
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Nov 15-10:38 AM
Nov 19-10:29 AM
25
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
How many drink tea & cola only ?
How many drink none of the 3 ?
Nov 27-10:49 PM
Nov 27-10:49 PM
26
Chapter 5 Section 3 day 2 2016s Notes.notebook
April 18, 2016
Dec 7-8:26 AM
27