Chapter 5 Section 3 day 1 2016s.notebook
April 15, 2016
Honors Statistics
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Apr 9-2:22 PM
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Chapter 5 Section 3 day 1 2016s.notebook
April 15, 2016
3. Review Homework C5#5
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Dec 1-5:05 PM
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Chapter 5 Section 3 day 1 2016s.notebook
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A Skip 52, 55
How do you want it - the crystal mumbo-jumbo
or statistical probability?
Apr 25-10:55 AM
Preparing for the GMAT A company that offers courses to prepare students for the Graduate
Management Admission Test (GMAT) has the following information about its customers: 20%
are currently undergraduate students in business; 15% are undergraduate students in other fields
of study; 60% are college graduates who are currently employed; and 5% are college graduates
who are not employed. Choose a customer at random.
P(Undergrad and Business) = 0.20 P(Undergrad and other) = 0.15
P(Grad and Employed) = 0.60
P(Grad and not employed) = 0.05
Notice that all the Probabilities add up to 1.00
(a) What’s the probability that the customer is currently an undergraduate? Which rule of
probability did you use to find the answer?
P(Undergrad) = P(Undergrad and Business) +
P(Undergrad and other) = 0.35 or 35%
I can add these because the events (Undergrad Bus) and
(Undergrad other) are mutually exclusive.
(b) What’s the probability that the customer is not an undergraduate business student? Which
rule of probability did you use to find the answer?
NOT
Law of complements
P(Undergrad Business ) = 1- 0.20 = 0.80
c
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Chapter 5 Section 3 day 1 2016s.notebook
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Sampling senators The two-way table below describes the members of the U.S Senate in a recent year.
60
40
17
83
100
If we select a U.S. senator at random, what’s the probability that the senator is
60
(a) a Democrat? P(Democrat) = --------- = 0.60
100
(b) a female?
17
P(Female) = --------- = 0.17
100
(c) a female and a Democrat?
13
P(Female and Democrat) = --------- = 0.13
100
(d) a female or a Democrat?
Two ways to do this problem
Way 1 - Using the General Addition formula
Way 2 - Using the table counts
P(Female or Democrat) = P(Female) + P(Democrat) - P(Female and Democrat)
60
17
13
64
P(Female or Democrat) = -------- + -------- - -------- = ------- = 0.64
100
100
100
100
13 + 4 + 47
64
P(Female or Democrat) = --------------------- = ------- = 0.64
100
100
Nov 15-6:09 PM
Playing cards Shuffle a standard deck of playing cards and deal one card.
Define events J: getting a jack, and R: getting a red card.
(a) Construct a two-way table that describes the sample space in terms of events
J and R.
(b) Find P(J) and P(R).
Jack
JackC
Red
2
24
26
RedC
2
24
26
4
48
52
4
26
P(J) = -------- = 0.077
P(R) = ---------- = 0.5
52
52
(c) Describe the event “J and R” in words. Then find P(J and R).
2
The card is a red jack or the card is red and a jack. P(J and R) = -------- = 0.038
52
(d) Explain why P(J or R) ≠ P(J) + P(R). Then use the general addition rule to
compute P(J or R).
The events card is red and card is a jack are not mutually exclusive ...
thus one will count two cards twice unless using the general probability addition formula.
2 + 2 + 24
28
P(J U R) = ---------------- = ------- = 0.538
52
52
OR
4
26
2
28
52
52
52
52
P(J U R) = ------ + ------- - ------- = ------- = 0.538
Nov 15-6:00 PM
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Chapter 5 Section 3 day 1 2016s.notebook
April 15, 2016
Who eats breakfast? Refer to Exercise 49.
(a) Construct a Venn diagram that models the chance process using events B: eats
breakfast regularly, and M: is male.
B
M
110
130
190
165
(b) Find P(B ∪ M). Interpret this value in context.
430
110+ 190+130
P(B U M) = ---------------- = ------- = 0.723
595
595
OR
300
320
190
430
595
595
595
595
P(B U M) = ------ + ------- - ------- = ------- = 0.723
the probabililty that person is a male or eats breakfast regularly (or both) = 72.3%
(c) Find P(BC ∩ MC). Interpret this value in context.
165
P(BC ∩ MC) = -------= 0.277
595
the probabililty that a person is not a male and does not eat breakfast is 27.7%
Nov 15-6:33 PM
Sampling senators Refer to Exercise 50.
60
40
83
17
100
(a) Construct a Venn diagram that models the chance process using events R: is a
Republican, and F: is female.
R
F
4
36
13
47
(b) Find P(R ∪ F). Interpret this value in context.
36 +4 + 13
53
100
100
P(R U F) = ----------- = ------- = 0.53
OR
40
17
4
53
100
100
100
100
P(R U F) = ------ + ------- - ------- = ------- = 0.53
the probabililty that a senator is a Republican or a Female (or both) = 53%
(c) Find P(RC ∩ FC). Interpret this value in context.
47
P(RC ∩ FC) = -------- = 0.47
100
the probabililty that a senator is a not Republican and not Female = 47%
Nov 15-6:33 PM
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Chapter 5 Section 3 day 1 2016s.notebook
April 15, 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.
(a) Make a two-way table for this chance process.
FACE
NF
UTube 0.66
0.07
NU
0.19
0.08
0.85
0.15
0.73
0.27
1.00
(b) Construct a Venn diagram to represent this setting.
Face
UT
0.07
0.66
0.19
0.23
(c) Consider the event that the randomly selected college student has posted a
profile on Facebook or uses YouTube regularly. Write this event in symbolic form
based on your Venn diagram in part (b).
P(Face or UTube) = P(F U T) =
(d) Find the probability of the event described in part (c). Explain your method.
P(F U T) = P(F) + P(T) - P(F ∩ T) = 0.85 + 0.73 - 0.66 = 0.92
OR USing VENN DIAGRAM
P(F U T) = 0.07 + 0.66 + 0.19 = 0.92
Nov 15-6:33 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 respondents were graduate students who said that
they used PCs as their main computers. Suppose we select a student at
random from among those who were part of the census.
(a) Make a two-way table for this chance process.
MAC
PC
0.30
0.37
0.67
Grad 0.10
0.23
0.33
0.40
0.60
1.00
Und
(b) Construct a Venn diagram to represent this setting.
MAC
Und
0.37
0.30
0.10
0.23
(c) Consider the event that the randomly selected student is a graduate
student and uses a Mac. Write this event in symbolic form based on your
Venn diagram in part (b).
P(Graduate and MAC) = P(Uc and MAC)
(d) Find the probability of the event described in part (c). Explain your
method.
P(Graduate and MAC) = P(Uc and MAC) = 0.10
ALTERNATIVE VENN DIAGRAM
MAC
Grad
0.23
0.10
0.30
0.37
c and d) P(G and MAC) = P(G ∩ M) = 0.10
Nov 15-6:33 PM
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Chapter 5 Section 3 day 1 2016s.notebook
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Chapter 5 Section 3 day 1 2016s.notebook
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Please place the following in your pocket folder:
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Chapter 5 Section 3 day 1 2016s.notebook
Conditional Probability =
April 15, 2016
P(both events occur)
P(given event occurs)
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May 3-6:12 PM
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(given landline, also cell phone)
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Chapter 5 Section 3 day 1 2016s.notebook
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(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
Worksheets ??
How do you want it - the crystal mumbo-jumbo
or statistical probability?
Apr 25-10:55 AM
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Chapter 5 Section 3 day 1 2016s.notebook
April 15, 2016
0.28
0.14
16
58
0.276
T
P(H ∩ T) = 0
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