Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
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
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
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
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.
Get tutor help
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.
Get tutor help
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.
Get tutor help
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.
Get tutor help
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
