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Math Problems
Precalculus
Identify independent events
In an experiment, the probability that event
A
A
A
occurs is
8
9
\frac{8}{9}
9
8
, the probability that event
B
B
B
occurs is
5
6
\frac{5}{6}
6
5
, and the probability that events
A
A
A
and
B
B
B
both occur is
20
27
\frac{20}{27}
27
20
. Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
2
7
\frac{2}{7}
7
2
, the probability that event
B
B
B
occurs is
2
7
\frac{2}{7}
7
2
, and the probability that events
A
A
A
and
B
B
B
both occur is
4
49
\frac{4}{49}
49
4
. Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
4
9
\frac{4}{9}
9
4
, the probability that event
B
B
B
occurs is
6
7
\frac{6}{7}
7
6
, and the probability that events
A
A
A
and
B
B
B
both occur is
8
21
\frac{8}{21}
21
8
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
6
7
\frac{6}{7}
7
6
, the probability that event
B
B
B
occurs is
8
9
\frac{8}{9}
9
8
, and the probability that events
A
A
A
and
B
B
B
both occur is
16
21
\frac{16}{21}
21
16
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
5
8
\frac{5}{8}
8
5
, the probability that event
B
B
B
occurs is
3
8
\frac{3}{8}
8
3
, and the probability that events
A
A
A
and
B
B
B
both occur is
15
64
\frac{15}{64}
64
15
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
2
3
\frac{2}{3}
3
2
, the probability that event
B
B
B
occurs is
1
3
\frac{1}{3}
3
1
, and the probability that events
A
A
A
and
B
B
B
both occur is
1
9
\frac{1}{9}
9
1
. Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
5
9
\frac{5}{9}
9
5
, the probability that event
B
B
B
occurs is
5
7
\frac{5}{7}
7
5
, and the probability that events
A
A
A
and
B
B
B
both occur is
25
63
\frac{25}{63}
63
25
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
1
7
\frac{1}{7}
7
1
, the probability that event
B
B
B
occurs is
2
7
\frac{2}{7}
7
2
, and the probability that events
A
A
A
and
B
B
B
both occur is
2
49
\frac{2}{49}
49
2
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
2
3
\frac{2}{3}
3
2
, the probability that event
B
B
B
occurs is
3
7
\frac{3}{7}
7
3
, and the probability that events
A
A
A
and
B
B
B
both occur is
1
7
\frac{1}{7}
7
1
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
1
8
\frac{1}{8}
8
1
, the probability that event
B
B
B
occurs is
1
7
\frac{1}{7}
7
1
, and the probability that events
A
A
A
and
B
B
B
both occur is
1
56
\frac{1}{56}
56
1
. Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
1
4
\frac{1}{4}
4
1
, the probability that event
B
B
B
occurs is
1
3
\frac{1}{3}
3
1
, and the probability that events
A
A
A
and
B
B
B
both occur is
1
12
\frac{1}{12}
12
1
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
2
5
\frac{2}{5}
5
2
, the probability that event
B
B
B
occurs is
5
9
\frac{5}{9}
9
5
, and the probability that events
A
A
A
and
B
B
B
both occur is
1
9
\frac{1}{9}
9
1
. Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
6
7
\frac{6}{7}
7
6
, the probability that event
B
B
B
occurs is
3
8
\frac{3}{8}
8
3
, and the probability that events
A
A
A
and
B
B
B
both occur is
9
28
\frac{9}{28}
28
9
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
4
9
\frac{4}{9}
9
4
, the probability that event
B
B
B
occurs is
5
9
\frac{5}{9}
9
5
, and the probability that events
A
A
A
and
B
B
B
both occur is
20
81
\frac{20}{81}
81
20
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
1
4
\frac{1}{4}
4
1
, the probability that event
B
B
B
occurs is
3
7
\frac{3}{7}
7
3
, and the probability that events
A
A
A
and
B
B
B
both occur is
3
28
\frac{3}{28}
28
3
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
3
8
\frac{3}{8}
8
3
, the probability that event
B
B
B
occurs is
5
6
\frac{5}{6}
6
5
, and the probability that events
A
A
A
and
B
B
B
both occur is
5
16
\frac{5}{16}
16
5
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
5
9
\frac{5}{9}
9
5
, the probability that event
B
B
B
occurs is
2
5
\frac{2}{5}
5
2
, and the probability that events
A
A
A
and
B
B
B
both occur is
1
9
\frac{1}{9}
9
1
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
1
2
\frac{1}{2}
2
1
, the probability that event
B
B
B
occurs is
4
7
\frac{4}{7}
7
4
, and the probability that events
A
A
A
and
B
B
B
both occur is
1
7
\frac{1}{7}
7
1
. Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
3
7
\frac{3}{7}
7
3
, the probability that event
B
B
B
occurs is
2
3
\frac{2}{3}
3
2
, and the probability that events
A
A
A
and
B
B
B
both occur is
1
7
\frac{1}{7}
7
1
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
5
7
\frac{5}{7}
7
5
, the probability that event
B
B
B
occurs is
3
7
\frac{3}{7}
7
3
, and the probability that events
A
A
A
and
B
B
B
both occur is
15
49
\frac{15}{49}
49
15
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
5
7
\frac{5}{7}
7
5
, the probability that event
B
B
B
occurs is
2
9
\frac{2}{9}
9
2
, and the probability that events
A
A
A
and
B
B
B
both occur is
10
63
\frac{10}{63}
63
10
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
1
5
\frac{1}{5}
5
1
, the probability that event
B
B
B
occurs is
1
6
\frac{1}{6}
6
1
, and the probability that events
A
A
A
and
B
B
B
both occur is
1
30
\frac{1}{30}
30
1
. Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
5
9
\frac{5}{9}
9
5
, the probability that event
B
B
B
occurs is
3
5
\frac{3}{5}
5
3
, and the probability that events
A
A
A
and
B
B
B
both occur is
2
9
\frac{2}{9}
9
2
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
7
9
\frac{7}{9}
9
7
, the probability that event
B
B
B
occurs is
3
7
\frac{3}{7}
7
3
, and the probability that events
A
A
A
and
B
B
B
both occur is
2
9
\frac{2}{9}
9
2
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
5
7
\frac{5}{7}
7
5
, the probability that event
B
B
B
occurs is
1
7
\frac{1}{7}
7
1
, and the probability that events
A
A
A
and
B
B
B
both occur is
5
49
\frac{5}{49}
49
5
. Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
6
7
\frac{6}{7}
7
6
, the probability that event
B
B
B
occurs is
5
7
\frac{5}{7}
7
5
, and the probability that events
A
A
A
and
B
B
B
both occur is
30
49
\frac{30}{49}
49
30
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
4
9
\frac{4}{9}
9
4
, the probability that event
B
B
B
occurs is
3
4
\frac{3}{4}
4
3
, and the probability that events
A
A
A
and
B
B
B
both occur is
2
9
\frac{2}{9}
9
2
. Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
7
9
\frac{7}{9}
9
7
, the probability that event
B
B
B
occurs is
2
7
\frac{2}{7}
7
2
, and the probability that events
A
A
A
and
B
B
B
both occur is
1
9
\frac{1}{9}
9
1
. Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
4
9
\frac{4}{9}
9
4
, the probability that event
B
B
B
occurs is
1
2
\frac{1}{2}
2
1
, and the probability that events
A
A
A
and
B
B
B
both occur is
1
9
\frac{1}{9}
9
1
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
1
3
\frac{1}{3}
3
1
, the probability that event
B
B
B
occurs is
2
3
\frac{2}{3}
3
2
, and the probability that events
A
A
A
and
B
B
B
both occur is
1
9
\frac{1}{9}
9
1
. Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
1
8
\frac{1}{8}
8
1
, the probability that event
B
B
B
occurs is
6
7
\frac{6}{7}
7
6
, and the probability that events
A
A
A
and
B
B
B
both occur is
3
28
\frac{3}{28}
28
3
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
5
7
\frac{5}{7}
7
5
, the probability that event
B
B
B
occurs is
1
4
\frac{1}{4}
4
1
, and the probability that events
A
A
A
and
B
B
B
both occur is
5
28
\frac{5}{28}
28
5
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
3
4
\frac{3}{4}
4
3
, the probability that event
B
B
B
occurs is
5
7
\frac{5}{7}
7
5
, and the probability that events
A
A
A
and
B
B
B
both occur is
15
28
\frac{15}{28}
28
15
. Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
2
3
\frac{2}{3}
3
2
, the probability that event
B
B
B
occurs is
4
5
\frac{4}{5}
5
4
, and the probability that events
A
A
A
and
B
B
B
both occur is
8
15
\frac{8}{15}
15
8
.
\newline
Are
A
A
A
and
B
B
B
independent events?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
Let
X
X
X
have the probability density function given by:
\newline
f
X
(
x
)
=
0.5
e
−
∣
x
∣
f_{X}(x)=0.5e^{-|x|}
f
X
(
x
)
=
0.5
e
−
∣
x
∣
where
−
∞
<
x
<
∞
-\infty < x < \infty
−
∞
<
x
<
∞
.
\newline
What is the probability that
∣
x
∣
|x|
∣
x
∣
falls between
2
2
2
and
4
4
4
?
\newline
Round your answer to three decimal places.
\newline
Pick ONE option
\newline
(A)
0.117
0.117
0.117
\newline
(B)
0.018
0.018
0.018
\newline
(C)
0.135
0.135
0.135
\newline
(D)
0.068
0.068
0.068
Get tutor help
Given that events A and B are independent with
P
(
A
)
=
0.95
P(A)=0.95
P
(
A
)
=
0.95
and
P
(
B
)
=
0.4
P(B)=0.4
P
(
B
)
=
0.4
, determine the value of
P
(
A
∣
B
)
P(A \mid B)
P
(
A
∣
B
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
Get tutor help
Given that events A and B are independent with
P
(
A
)
=
0.43
P(A)=0.43
P
(
A
)
=
0.43
and
P
(
B
)
=
0.3
P(B)=0.3
P
(
B
)
=
0.3
, determine the value of
P
(
B
∣
A
)
P(B \mid A)
P
(
B
∣
A
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
Get tutor help
Given that events A and B are independent with
P
(
A
)
=
0.46
P(A)=0.46
P
(
A
)
=
0.46
and
P
(
B
)
=
0.3
P(B)=0.3
P
(
B
)
=
0.3
, determine the value of
P
(
A
∣
B
)
P(A \mid B)
P
(
A
∣
B
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
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Given that events A and B are independent with
P
(
A
)
=
0.1
P(A)=0.1
P
(
A
)
=
0.1
and
P
(
A
P(A
P
(
A
and
B
)
=
0.041
B)=0.041
B
)
=
0.041
, determine the value of
P
(
B
)
P(B)
P
(
B
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
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Given that events A and B are independent with
P
(
A
)
=
0.79
P(A)=0.79
P
(
A
)
=
0.79
and
P
(
B
)
=
0.6
P(B)=0.6
P
(
B
)
=
0.6
, determine the value of
P
(
A
P(A
P
(
A
and
B
)
B)
B
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
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Given that events A and B are independent with
P
(
A
)
=
0.72
P(A)=0.72
P
(
A
)
=
0.72
and
P
(
B
)
=
0.1
P(B)=0.1
P
(
B
)
=
0.1
, determine the value of
P
(
A
∩
B
)
P(A \cap B)
P
(
A
∩
B
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
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Given that events A and B are independent with
P
(
A
)
=
0.6
P(A)=0.6
P
(
A
)
=
0.6
and
P
(
B
)
=
0.72
P(B)=0.72
P
(
B
)
=
0.72
, determine the value of
P
(
A
∩
B
)
P(A \cap B)
P
(
A
∩
B
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
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Given that events A and B are independent with
P
(
A
)
=
0.5
P(A)=0.5
P
(
A
)
=
0.5
and
P
(
B
)
=
0.37
P(B)=0.37
P
(
B
)
=
0.37
, determine the value of
P
(
A
∩
B
)
P(A \cap B)
P
(
A
∩
B
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
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