Download Chapter 6 Review

Quiz 6.3C
Here are the counts (in thousands) of earned
degrees in the United States in a recent year,
classified by level and by the sex of the degree
recipient:
Bachelor’s Master’s
Professiona
l
Doctorat
e
Total
Female
616
194
30
16
856
Male
529
171
44
26
770
Total
1145
365
74
42
1626
Chapter 6 Review
1. If a peanut M&M is chosen at random, the chances of it
being of a particular color are shown in the table below.
Color
Brown Red
Probability .2
.2
Yellow Green Orange
.2
.2
.1
Blue
The probability of randomly drawing a blue peanut M&M is
(a)
0.1
(b)
0.2
(c)
0.3
(d)
1.0
(e)
According to this distribution, it’s impossible to
draw a blue peanut M&M.
2. Which of the following pairs of events are
disjoint (mutually exclusive)?
(a)
(b)
(c)
(d)
A: the odd numbers; B: the number 3
A: the even numbers; B: the numbers
greater than 12
A: the numbers less than 3; B: all
negative numbers
A: the numbers above 50; B: the
numbers less than –50
Reminder
3. Data show that 14% of the civilian labor force has
at least 4 years of college and that 10% of the labor
force works as laborers or operators of machines or
vehicles. Can you conclude that because
(0.14)(0.10) = .014 about 1% of the labor force are
college-educated laborers or operators?
(a)
(b)
(c)
(d)
(e)
Yes, by the multiplication rule
Yes, by conditional probabilities
Yes, by the law of large numbers
No, because the events are not
independent
No, because the events are not mutually
exclusive
Reminder
4. Which of the following are true?
I. The sum of the probabilities in a probability
distribution can be any number between 0 and 1.
II. The probability of the union of two events is the sum of
the probabilities of those events.
III. The probability that an event happens is equal to
1 – (the probability that the event does not happen).
(a)
I and II only
(b)
I and III only
(c)
II and III only
(d)
I, II, and III
(e)
None of the above gives the complete set of true
responses
5. If AB = S (sample space), P(A and Bc) =
0.15, and P(Ac) = 0.40, then P(B) =
(a) 0.15
(b) 0.45
(c) 0.65
(d) 0.85
A bag contains 4 orange tags
numbered 1 – 4 and two
black tags numbered 1 – 2.
One tag is drawn at random.
6. List the sample space.
Calculate the following probabilities.
7. P(orange)
8. P(even number)
9. P(Black and odd)
10. P(orange or odd)
11. P(neither orange nor odd)
A bag contains 4 orange tags
numbered 1 – 4 and two
black tags numbered 1 – 2.
One tag is drawn at random.
12. P(odd|orange)
13. P(orange|even)
14. P(<3|odd)
15. Suppose the probability of eating popcorn
is .4 and that the probability of drinking
Sprite is .8. Further suppose that the
probability of eating popcorn and drinking
Sprite is .32. Are these two events
independent? How do you know?
Consider this experiment: the letters in the word
MISSISSIPPI are printed on square pieces of
tagboard (same size squares) with one letter per
card. The eleven letter cards are then placed in
a top hat, and one letter card is randomly
chosen (without looking) from the hat with
replacement.
16. List the sample space of all possible outcomes.
S={
}
17. Make a table that shows the set of outcomes
(X) and the probability of each outcome:
Outcomes (X)
P(X)
Outcomes (x)
P(X)
I
4/11
M
1/11
P
2/11
S
4/11
18. Consider the following events:
C: a consonant
V: a vowel
F: the letter chosen falls in the first half of the alphabet (A
to M).
List the outcomes and give the probability:
a) V = { }
P(V) =
b) C = { }
P(C) =
c) F = { }
P(F) =
d) V or F = { }
P(V or F) =
e) complement of C = { }
P(Cc) =
19. Are events V and F independent? Explain.
The chart below describes the probabilities of the age in years
and the sex of randomly selected students.
Age
14-17
18-24
25-34
≥35
Male
.01
.30
.12
.04
Female .01
.30
.13
.09
20. What is the probability the student is male?
21. What is the conditional probability that the student is
male given that the student is between 18 – 24?
22. What is the probability that the student is either male or
between 18 – 24?
23. If four cards are drawn from a standard
deck of 52 playing cards and not
replaced, find the probability of getting at
least one spade.
24. If four dice are rolled, find the probability
of getting quads – 1,1,1,1 or 2,2,2,2, etc.
Reminder
 Disjoint – mutually exclusive (no
outcomes in common, never occur
simultaneously, one happens then the
other.
 Independent – knowing one outcome
doesn’t change the other outcome.
Answers
1.A
2. D
3. D
4. E
5. D
6. O1, O2, O3,
O4, B1, B2
7. 4/6 = 2/3
8. 3/6 =1/2
9. 1/6
10. 5/6
11. 1/6
12. 1/2
13. 2/3
14. 2/3
15. Yes
.4(.8) = .32
16. M, I, S, P
17. See
slide
18. a. I; 4/11
b. M,P, S; 7/11
c. I, M; 5/11
d. I, M; 5/11
e. I; 4/11
19. no;
4/11 ≠
(4/11)(5/11)
20. .47
21. P(M|18-24)
=½
22. .47 +
.30 = .77
23. 1 - P(0
24. 6/1296
spades) = 1or 1/216
[(39/52)(38/51)(37
/50)(36/49)] = 1.304 = .696