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Math Problems
Grade 8
Identify independent and dependent events
Vivian calls a bakery and orders a custom cake with a certain design. Later that day, Tommy calls to order a custom cake.
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Are these two events dependent or independent?
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Choices:
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(A)dependent
\newline
(B)independent
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For homework, a teacher instructs her students to choose a county in their state for a social studies project. Since they live in a small state, repeats are allowed.
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Are these two events dependent or independent?
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Choices:
\newline
(A) dependent
\newline
(B) independent
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Students are auditioning for roles in the school musical. Each student must come ready to perform a song of his or her choice in front of the judges.
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Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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Students in a composition class may select certain topics on which to write an essay. Repeats are allowed, and they do not need to inform the teacher of their choice prior to the due date of the essay.
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Are these two events dependent or independent?
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Choices:
\newline
(A)dependent
\newline
(B)independent
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Rob picks a marble at random. Without putting the first marble back, he picks a second marble at random.
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Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
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(B) independent
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Seth chooses a colored marble from a mixed bag and writes down the color. Seth leaves it out and then draws another.
\newline
Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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Without discussing their choices, Regan and Lola pick professions to discuss on career day. The students have the option of discussing the same profession.
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Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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Liam and Dave see a movie together. Liam picks a chair first, then Dave does.
\newline
Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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A babysitter tells two brothers that she will get each one's favorite candy when she goes to the grocery store. The older brother whispers his preference in the babysitter's ear, and then the younger brother does the same.
\newline
Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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Harry and Isaac need to schedule appointments with the same doctor. Harry calls in the morning and picks one of the open appointment times. In the afternoon, Isaac calls to schedule one of the remaining appointment times.
\newline
Are these two events dependent or independent?
\newline
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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Josie is shopping for a wedding gift for her friends, who have registered at a department store. Some of the items on the registry have already been purchased by other wedding guests.
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Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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Sally picks a card at random, puts it back, and then picks another card at random.
\newline
Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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Karen picks a card at random. Without putting the first card back, she picks a second card at random.
\newline
Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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Without looking, Zack chooses a colored marble from a mixed bag of marbles, writes down the color, and returns it to the bag. Then, he draws another marble without looking.
\newline
Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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Rosanne picks a marble at random, puts it back, and then picks another marble at random.
\newline
Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
Get tutor help
Harper selects a box of cereal for her family at the supermarket. Across town, Rhianna also happens to pick out a box of cereal for her own family.
\newline
Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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A street magician asks a volunteer to pick a card, which is put back into the deck at the end of the trick. A few minutes later, the magician shuffles the deck and asks a different person to choose a card.
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Are these two events dependent or independent?
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Choices:
\newline
(A) dependent
\newline
(B) independent
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Eve and Kiera are preparing to play a board game together. Eve chooses one of
6
6
6
colored tokens to use as her marker. Kiera chooses next.
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Are these two events dependent or independent?
\newline
Choices:
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(A) dependent
\newline
(B) independent
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Baldwin, a teacher, is asking his students to write down their favorite colors so they may graph the results.
\newline
Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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A group of friends is drawing names for a gift exchange. Mitch chooses, and then Emilio selects next.
\newline
Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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Sofia is conducting a survey about favorite ice cream flavors. Sofia surveys
99
99
99
random people and then decides to ask one more.
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Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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Brandon and Lee pick chairs at the same dinner table. Brandon picks first, and Lee goes second.
\newline
Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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Greta and Luca pick out seats at the school orchestra concert. Greta picks first, then it is Luca's turn.
\newline
Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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Students in a classroom are voting for class president by secret ballot. Isaiah submits a ballot, and then Layla does.
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Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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During a game of roulette, a wheel is spun and a ball drops randomly into one of the wheel's numbered compartments. Then the process is repeated with another random spin.
\newline
Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
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Lucy and Norma are rolling dice to see who goes first in a board game.
\newline
Are these two events dependent or independent?
\newline
Choices:
\newline
(A) dependent
\newline
(B) independent
Get tutor help
Given that events A and B are independent with
P
(
A
)
=
0.73
P(A)=0.73
P
(
A
)
=
0.73
and
P
(
B
∣
A
)
=
0.6
P(B \mid A)=0.6
P
(
B
∣
A
)
=
0.6
, 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
)
=
0.9
P(A)=0.9
P
(
A
)
=
0.9
and
P
(
B
)
=
0.21
P(B)=0.21
P
(
B
)
=
0.21
, 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
)
=
0.25
P(A)=0.25
P
(
A
)
=
0.25
and
P
(
B
)
=
0.88
P(B)=0.88
P
(
B
)
=
0.88
, 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
)
=
0.3
P(A)=0.3
P
(
A
)
=
0.3
and
P
(
B
∣
A
)
=
0.89
P(B \mid A)=0.89
P
(
B
∣
A
)
=
0.89
determine the value of
P
(
B
)
P(B)
P
(
B
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
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