16.
-/1 points WaneFM7 7.1.025.
My Notes
Ask Your Teacher
Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 3; B: the numbers add to 6; C: at least one of the numbers is 5; and D: the numbers do not add
to 8. Express the given event in symbolic form. HINT (See Example 5.]
The numbers do not add to 6.
B
D
D'
B'
BUD
How many elements does it contain?
17.
-/1 points WaneFM7 7.1.027.
My Notes
Ask Your Teacher
Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 7; C: at least one of the numbers is 4; and D: the numbers do not add
to 11. Express the given event in symbols. HINT [See Example 5.]
The numbers do not add up to 7, but they do add up to 11.
BUD
B'n D
B'UD
BnD
B' n D'
How many elements does it contain?
20.
-/1 points WaneFM7 7.1.050.
My Notes
Ask Your Teacher
The following table shows the results of a survey of authors by a (fictitious) publishing company. HINT [See Example 5.]
New Authors
Established Authors
Total
Successful
6
14
20
Unsuccessful
8
6
14
Total
14
20
34
Consider the following events: S: an author is successful; U: an author is unsuccessful; N: an author is new; and E: an author is established.
Describe the events NnU and NUU in words.
NnU is the event that an author is
---Select---
NUU is the event that an author is ---Select---
Use the table to compute n(N n U) and n(N U U).
n(Na U) =
n(NU U) =
21.
-/1 points WaneFM7 7.1.070.
My Notes
Ask Your Teacher
Use counting arguments from the preceding chapter.
My couch potato friend enjoys sitting in front of the TV and grabbing handfuls of 5 chocolates at random from his snack jar. Unbeknownst to him, I have replaced one of the 16 chocolates in his jar
with a cashew. (He hates cashews with a passion.) How many possible outcomes are there the first time he grabs 5 chocolates?
outcomes
How many of these include the cashew?
outcomes
22.
-/1 points WaneFM7 7.2.037.
My Notes
Ask Your Teacher
The following table shows the results of a survey of 500 authors by a publishing company.
New Authors
Established Authors
Total
Successful
50
115
165
Unsuccessful
100
235
335
Total
150
350
500
Compute the relative frequency of the given event if an author as specified is chosen at random.
An author is established and successful.
23.
-/1 points WaneFM7 7.2.039.
My Notes
Ask Your Teacher
The following table shows the results of a survey of 100 authors by a publishing company.
New Authors
Established Authors
Total
Successful
4.
27
31
Unsuccessful
20
49
69
Total
24
76
100
Compute the relative frequency of the given event if an author as specified is chosen at random.
An author is a new author.
24.
-/1 points WaneFM7 7.2.043.
My Notes
Ask Your Teacher
The following table shows the results of a survey of 200 authors by a publishing company.
New Authors
Established Authors
Total
Successful
16
50
66
Unsuccessful
36
98
134
Total
52
148
200
Compute the relative frequency of the given event if an author as specified is chosen at random.
A successful author is established.
25.
-/1 points WaneFM7 7.2.045.
My Notes
Ask Your Teacher
The following table shows the results of a survey of 400 authors by a publishing company.
New Authors
Established Authors
Total
Successful
28
96
124
Unsuccessful
76
200
276
Total
104
296
400
Compute the relative frequency of the given event if an author as specified is chosen at random.
An established author is successful.
26.
-/1 points WaneFM7 7.3.001.
My Notes
Ask Your Teacher
Complete the following probability distribution table and then calculate the stated probabilities. HINT [See Quick Example 5.]
Outcome
a
b
C
d
e
Probability
0.3
0.01
0.4
0.09
(a) Pl{a, c, e})
P({a, c, e}) =
(b) P(EU F), where E = {a, c, e} and F = {b, c, e}
P(EU F) =
(c) P(E'), where E is as in part (b)
P(E)
=
(d) P(En F), where E and F are as in part (b)
P(En F) =
27.
-/1 points WaneFM7 7.3.020.
My Notes
Ask Your Teacher
If two indistinguishable dice are rolled, what is the probability of the event {(4,4), (3, 4), (1,4)}? HINT [See Example 2.]
What is the corresponding event for a pair of distinguishable dice?
{(4,4), (3, 4), (1, 4)}
{(4,4), (3, 4), (1, 4), (4, 1), (4,3)}
{(4,4), (3, 3), (1, 1), (4, 1), (4,3)}
{(3, 4), (1, 4), (4, 1), (4,3)}
{(3, 4), (1,4)}
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