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Math Problems
Algebra 2
Independence and conditional probability
In an experiment, the probability that event
A
A
A
occurs is
4
9
\frac{4}{9}
9
4
and the probability that event
B
B
B
occurs is
8
9
\frac{8}{9}
9
8
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
2
5
\frac{2}{5}
5
2
and the probability that event
B
B
B
occurs is
3
5
\frac{3}{5}
5
3
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
1
2
\frac{1}{2}
2
1
and the probability that event
B
B
B
occurs is
4
9
\frac{4}{9}
9
4
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
3
7
\frac{3}{7}
7
3
and the probability that event
B
B
B
occurs is
3
8
\frac{3}{8}
8
3
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
3
5
\frac{3}{5}
5
3
and the probability that event
B
B
B
occurs is
1
8
\frac{1}{8}
8
1
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur? Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
4
9
\frac{4}{9}
9
4
and the probability that event
B
B
B
occurs is
7
8
\frac{7}{8}
8
7
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
1
8
\frac{1}{8}
8
1
and the probability that event
B
B
B
occurs is
7
8
\frac{7}{8}
8
7
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
5
7
\frac{5}{7}
7
5
and the probability that event
B
B
B
occurs is
4
5
\frac{4}{5}
5
4
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
1
6
\frac{1}{6}
6
1
and the probability that event
B
B
B
occurs is
4
7
\frac{4}{7}
7
4
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
8
9
\frac{8}{9}
9
8
and the probability that event
B
B
B
occurs is
4
9
\frac{4}{9}
9
4
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
6
7
\frac{6}{7}
7
6
and the probability that event
B
B
B
occurs is
1
9
\frac{1}{9}
9
1
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
3
4
\frac{3}{4}
4
3
and the probability that event
B
B
B
occurs is
7
9
\frac{7}{9}
9
7
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
4
9
\frac{4}{9}
9
4
and the probability that event
B
B
B
occurs is
4
5
\frac{4}{5}
5
4
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
4
5
\frac{4}{5}
5
4
and the probability that event
B
B
B
occurs is
1
5
\frac{1}{5}
5
1
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
5
9
\frac{5}{9}
9
5
and the probability that event
B
B
B
occurs is
1
5
\frac{1}{5}
5
1
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
5
6
\frac{5}{6}
6
5
and the probability that event
B
B
B
occurs is
2
9
\frac{2}{9}
9
2
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
3
7
\frac{3}{7}
7
3
and the probability that event
B
B
B
occurs is
1
8
\frac{1}{8}
8
1
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
2
5
\frac{2}{5}
5
2
and the probability that event
B
B
B
occurs is
2
3
\frac{2}{3}
3
2
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
6
7
\frac{6}{7}
7
6
and the probability that event
B
B
B
occurs is
1
8
\frac{1}{8}
8
1
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
3
7
\frac{3}{7}
7
3
and the probability that event
B
B
B
occurs is
4
7
\frac{4}{7}
7
4
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
7
9
\frac{7}{9}
9
7
and the probability that event
B
B
B
occurs is
3
8
\frac{3}{8}
8
3
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
1
4
\frac{1}{4}
4
1
and the probability that event
B
B
B
occurs is
5
6
\frac{5}{6}
6
5
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
4
9
\frac{4}{9}
9
4
and the probability that event
B
B
B
occurs is
4
9
\frac{4}{9}
9
4
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
5
9
\frac{5}{9}
9
5
and the probability that event
B
B
B
occurs is
4
9
\frac{4}{9}
9
4
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
1
3
\frac{1}{3}
3
1
and the probability that event
B
B
B
occurs is
1
7
\frac{1}{7}
7
1
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
4
5
\frac{4}{5}
5
4
and the probability that event
B
B
B
occurs is
3
5
\frac{3}{5}
5
3
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
1
9
\frac{1}{9}
9
1
and the probability that event
B
B
B
occurs is
1
3
\frac{1}{3}
3
1
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
\newline
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
2
5
\frac{2}{5}
5
2
and the probability that event
B
B
B
occurs is
3
4
\frac{3}{4}
4
3
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
\newline
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
2
5
\frac{2}{5}
5
2
and the probability that event
B
B
B
occurs is
7
8
\frac{7}{8}
8
7
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
\newline
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
8
9
\frac{8}{9}
9
8
and the probability that event
B
B
B
occurs is
1
6
\frac{1}{6}
6
1
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
2
9
\frac{2}{9}
9
2
and the probability that event
B
B
B
occurs is
8
9
\frac{8}{9}
9
8
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
1
5
\frac{1}{5}
5
1
and the probability that event
B
B
B
occurs is
1
7
\frac{1}{7}
7
1
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
4
5
\frac{4}{5}
5
4
and the probability that event
B
B
B
occurs is
4
5
\frac{4}{5}
5
4
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
2
9
\frac{2}{9}
9
2
and the probability that event
B
B
B
occurs is
2
9
\frac{2}{9}
9
2
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur? Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
4
5
\frac{4}{5}
5
4
and the probability that event
B
B
B
occurs is
6
7
\frac{6}{7}
7
6
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur? Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
6
7
\frac{6}{7}
7
6
and the probability that event
B
B
B
occurs is
7
9
\frac{7}{9}
9
7
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
1
6
\frac{1}{6}
6
1
and the probability that event
B
B
B
occurs is
5
9
\frac{5}{9}
9
5
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
4
9
\frac{4}{9}
9
4
and the probability that event
B
B
B
occurs is
1
7
\frac{1}{7}
7
1
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur? Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
7
8
\frac{7}{8}
8
7
and the probability that event
B
B
B
occurs is
3
7
\frac{3}{7}
7
3
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur?
\newline
Simplify any fractions.
Get tutor help
In an experiment, the probability that event
A
A
A
occurs is
2
5
\frac{2}{5}
5
2
and the probability that event
B
B
B
occurs is
2
7
\frac{2}{7}
7
2
. If
A
A
A
and
B
B
B
are independent events, what is the probability that
A
A
A
and
B
B
B
both occur? Simplify any fractions.
Get tutor help
Independent and Dependent Events
\newline
Suppose two cards are drawn randomly.
\newline
What is the probability of drawing two green cards, if the first card is NOT replaced before the second draw? Assume the first card drawn is green.
\newline
Show your answer as a fraction in lowest terms. Enter the numerator.
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If a box contains
4
4
4
Red balls,
5
5
5
Green balls,
6
6
6
Blue balls. Find the probability of
\newline
(a) Getting a green ball
\newline
(b) Getting a blue ball
\newline
(c) Non-red ball
Get tutor help
Let
g
(
x
)
=
tan
(
x
)
g(x)=\tan (x)
g
(
x
)
=
tan
(
x
)
.
\newline
Can we use the intermediate value theorem to say the equation
g
(
x
)
=
0
g(x)=0
g
(
x
)
=
0
has a solution where
π
4
≤
x
≤
3
π
4
\frac{\pi}{4} \leq x \leq \frac{3 \pi}{4}
4
π
≤
x
≤
4
3
π
?
\newline
Choose
1
1
1
answer:
\newline
(A) No, since the function is not continuous on that interval.
\newline
(B) No, since
0
0
0
is not between
g
(
π
4
)
g\left(\frac{\pi}{4}\right)
g
(
4
π
)
and
g
(
3
π
4
)
g\left(\frac{3 \pi}{4}\right)
g
(
4
3
π
)
.
\newline
(C) Yes, both conditions for using the intermediate value theorem have been met.
Get tutor help
Let
g
(
x
)
=
cos
(
x
)
g(x)=\cos (x)
g
(
x
)
=
cos
(
x
)
.
\newline
Can we use the intermediate value theorem to say the equation
g
(
x
)
=
0.8
g(x)=0.8
g
(
x
)
=
0.8
has a solution where
0
≤
x
≤
π
2
0 \leq x \leq \frac{\pi}{2}
0
≤
x
≤
2
π
?
\newline
Choose
1
1
1
answer:
\newline
(A) No, since the function is not continuous on that interval.
\newline
(B) No, since
0
0
0
.
8
8
8
is not between
g
(
0
)
g(0)
g
(
0
)
and
g
(
π
2
)
g\left(\frac{\pi}{2}\right)
g
(
2
π
)
.
\newline
(C) Yes, both conditions for using the intermediate value theorem have been met.
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Let
h
(
x
)
=
1
x
h(x)=\frac{1}{x}
h
(
x
)
=
x
1
.
\newline
Can we use the intermediate value theorem to say the equation
h
(
x
)
=
0.5
h(x)=0.5
h
(
x
)
=
0.5
has a solution where
−
1
≤
x
≤
1
-1 \leq x \leq 1
−
1
≤
x
≤
1
?
\newline
Choose
1
1
1
answer:
\newline
(A) No, since the function is not continuous on that interval.
\newline
(B) No, since
0
0
0
.
5
5
5
is not between
h
(
−
1
)
h(-1)
h
(
−
1
)
and
h
(
1
)
h(1)
h
(
1
)
.
\newline
(C) Yes, both conditions for using the intermediate value theorem have been met.
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What happens to the value of the expression
w
−
w
w-w
w
−
w
as
w
w
w
increases?
\newline
Choose
1
1
1
answer:
\newline
(A) It increases.
\newline
(B) It decreases.
\newline
(C) It stays the same.
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What happens to the value of the expression
3
e
3 e
3
e
as
e
e
e
increases?
\newline
Choose
1
1
1
answer:
\newline
(A) It increases.
\newline
(B) It decreases.
\newline
(C) It stays the same.
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What happens to the value of the expression
n
+
15
n+15
n
+
15
as
n
n
n
decreases?
\newline
Choose
1
1
1
answer:
\newline
(A) It increases.
\newline
(B) It decreases.
\newline
(C) It stays the same.
Get tutor help
What happens to the value of the expression
100
−
x
100-x
100
−
x
as
x
x
x
increases?
\newline
Choose
1
1
1
answer:
\newline
(A) It increases.
\newline
(B) It decreases.
\newline
(C) It stays the same.
Get tutor help
What happens to the value of the expression
150
−
j
150-j
150
−
j
as
j
j
j
decreases?
\newline
Choose
1
1
1
answer:
\newline
(A) It increases.
\newline
(B) It decreases.
\newline
(C) It stays the same.
Get tutor help
