# Cameron University Chapter 4 Independent or Dependent Exam

3/7/22, 9:36 AMMyOpenMath

Chapter 4 HW (Part 2)

Joao Guilherme Guercheski Duleba

Question 1

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Independent or Dependent

In each question below, you are given two events. Determine whether the events are Independent or

Dependent. Sort the questions into the appropriate category.

Hint: There are 4 questions in each category.

Question H

Independent

Dependent

Question C

Question B

Question F

Question D

Question A

Question E

Question G

Question A: Flipping a coin and tossing a die

Question B: Picking two digits from 0 to 9 when

the digits cannot repeat

Question C: Picking two books out of 10 books to

read for an English class

Question D: Drawing a card from a 52 card deck

then drawing a second card after replacing the

first card

Question E: From a group of 5 friends, choosing a Question F: Drawing a card from a 52 card deck

person to drive and another a person to sit in the then drawing a second card without replacing the

passenger seat

first card

Question G: Picking two digits from 0 to 9 when

the digits can repeat

Question Help:

Question H: Flipping a coin and then flipping the

coin again

Written Example

Question 2

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Are owning a bike and owning a car independent events? Why or why not?

Dependent,since knowing a person has one of these items changes the probability that the person

has the other item.

Dependent, since knowing that a person owns one of these items does not change the probability

of the person has the other item.

Independent,since knowing a person has one of these items changes the probability that the

person has the other item.

Independent, since knowing that a person owns one of these items does not change the

probability of the person has the other item.

Question 3

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Are owning a computer or tablet and paying for Internet service independent events? Why or why not?

Dependent, since knowing that a person owns one of these items does not change the probability

of the person has the other item.

Dependent,since knowing a person has one of these items changes the probability that the person

has the other item.

Independent, since knowing that a person owns one of these items does not change the

probability of the person has the other item.

Independent,since knowing a person has one of these items changes the probability that the

person has the other item.

Question 4

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A randomly selected card from a standard 52-card deck is noted. The card is then replaced, the deck is

shuffled, and a second card is selected and noted. What is the probability that both cards are Aces?

There is a

chance that two Aces are randomly selected (with replacement).

Question 5

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Use the information below to determine if events A and B are independent.

P (A) =

4

5

3

P (A ∣ B) =

5

independent

dependent

Question 6

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Use the information below to determine if events A and B are independent.

P (A) =

4

5

P (A ∣ B) = 0.80

dependent

independent

Question 7

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33 percent of young adult males play video games. 32 percent of young adult males have a full-time

job. 53 percent of young adult males that play video games also have a full-time job. Give your answers

as a decimal to 4 decimal places.

(a) What percent of young adult males play video games and have a full-time job?

(b) What percent of young adult males play video games or have a full-time job?

Question Help:

Video

Written Example

Question 8

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Round all answers to 4 decimal places.

a. A bag contains 4 green marbles, 8 black marbles, and 9 white marbles. If a marble is drawn from

the bag, replaced, and another marble is drawn, what is the probability of drawing first a green marble

and then a white marble?

b. A bag contains 8 blue marbles, 9 white marbles, and 4 black marbles. If two different marbles

are drawn from the bag , what is the probability of drawing first a blue marble and then a black

marble?

Question 9

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A die is rolled twice. What is the probability that a(n) 5 is rolled on the first roll and an even number on

the second roll?

The probability of rolling a(n) 5 on the first roll and an even number on the second roll is

.

Question Help:

Video

Question 10

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Determining the independence of events can sometimes be done by becoming familiar with the context

in which the events occur and the nature of the events. There are also some ways of determining

independence of events based on equivalent probabilities.

• Two events, A and B, are independent if `P(A and B) = P(A)*P(B)`

• Additionally, two events, A and B, are independent if `P(A|B)=(P(A and B))/(P(B))=P(A)`

Use these two ways of determining independent events to determine independence in the problem

below. You will be given one chance to answer correctly.

`P(A and B)=3/5`

`P(A)=1/2`

`P(B)=3/10`

A and B are

independent events

not independent events

Question 11

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Determining the independence of events can sometimes be done by becoming familiar with the context

in which the events occur and the nature of the events. There are also some ways of determining

independence of events based on equivalent probabilities.

• Two events, A and B, are independent if `P(A and B) = P(A)*P(B)`

• Additionally, two events, A and B, are independent if `P(A|B)=(P(A and B))/(P(B))=P(A)`

Use these two ways of determining independent events to determine independence in the problem

below. You will be given one chance to answer correctly.

`P(A)=1/2`

`P(A and B)=1/6`

`P(B)=1/3`

A and B are

not independent events

independent events

Question 12

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Determining the independence of events can sometimes be done by becoming familiar with the context

in which the events occur and the nature of the events. There are also some ways of determining

independence of events based on equivalent probabilities.

• Two events, A and B, are independent if `P(A and B) = P(A)*P(B)`

• Additionally, two events, A and B, are independent if `P(A|B)=(P(A and B))/(P(B))=P(A)`

Use these two ways of determining independent events to determine independence in the problem

below. You will be given one chance to answer correctly.

`P(A)=2/5`

`P(A and B)=1/4`

`P(B)=4/5`

A and B are

independent events

not independent events

Question 13

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Data gathered on the shopping patterns during the months of April and May of high school students from

Peanut Village revealed the following. 38% of students purchased a new pair of shorts (event H), 15% of

students purchased a new pair of sunglasses (event G), and 6% of students purchased both a pair of

shorts and a pair of sunglasses.

Find the probability that a student purchased a pair of sunglasses give that you know they purchased a

pair of shorts.

P(G | H) =

Question 14

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During a basketball game, Adrianna is shooting two free throws. She makes 80% of her free throws.

Assuming that her free throws are independent events, find the percent chance that she…

is in the groove and makes both free throws.

%

makes the first and then misses the second.

%

misses the first and then makes the second.

%

struggles and misses both of her free throws.

What is the sum of these four answers?

%

%

Question 15

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Suppose events A and B are independent. If `P(A \cap B)`=0.18 and `P(A)=`0.45, what is `P(B)=`?

Answer =

(Round your answer to 3 decimal places.)

Question 16

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According to the Center for Disease Control (CDC), 46.8% of Americans get a flu shot each season. What

is the probability that 3 randomly selected Americans get a flu shot? Round your answer to 4 decimal

places.

Question 17

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39.4% of US homes continue to use a landline in addition to cell phone service. 3 US homes are randomly

selected. What is the probability that at least one of the 3 continues to use a landline? Round your

answer to 4 decimal places.

Question 18

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The probabilities of events `A` and `B` respectively are given below.

`P(A)=0.44`

`P(B)=0.35`

Do not round answers.

1. If `A` and `B` are independent events, then

a) `P(A and B) =`

b) `P(A or B) =`

c) `P(B | A)=`

d) `P(A and barB)=`

e) `P(bar A and barB) =`

2. If `A` and `B` are mutually exclusive events, then

a) `P(A and B) =`

b) `P(A or B) =`

c) `P(A | B)=`

d) `P(barB and A)=`

e) `P(bar A and barB) =`

Question Help:

Video

Question 19

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Suppose you have an experiment where you flip a coin three times. You then count the number of

heads.

a) State the random variable.

Select an answer

b) Write the probability distribution for the number of heads.

Make sure to put the values of X from smallest to largest.

X

P(X)

c) If you were to draw a histogram for the number of heads, what shape would it be?

Select an answer

d) Find the mean number of heads.

Round final answer to 3 decimal places. Write your units in the second box.

Which of the following is the correct symbol for the mean of a probability distribution? ?

Which of the following is the correct interpretation of the mean?

Select an answer

e) Find the standard deviation for the number of heads.

Round final answer to 3 decimal places. Write your units in the second box.

Which of the following is the correct symbol for the standard deviation of a probability distribution?

?

f) Find the probability of having one or more heads.

Question Help:

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Question 20

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A local bakary has determined a probability distribution for the number of cheesecakes that they sell in

a given day.

X= #sold

0

5

10

Probability 0.18 0.33 0.08

15

20

…?

0.08

What is the probability of selling 15 cheesecakes in a given day?

What is the probability of selling at least 10 cheesecakes?

What is the probability of selling 5 or 15 chassescakes?

What is the probability of selling 25 cheesecakes?

What is the probability of selling at most 10 cheesecakes?

Give the expected number of cheesecakes sold in a day using the discrete probability distribution?

Question Help:

Video

Question 21

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The following table represents the probability of the number of cars owned by a college student. Give

your answer to at least 3 decimal places.

x

0

1

2

3

P(x)

0.45

0.34

0.13

0.08

a) Is this a valid discrete probability distribution? Select an answer

b) Find the mean number of cars owned.

c) Find the standard deviation of the number of cars owned.

d) Find `sigma^2` .

Question 22

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Consider the discrete random variable `X` given in the table below. Calculate the mean, variance, and

standard deviation of `X`.

`X`

P(`X`)

1

0.09

10

0.11

13

0.08

15

0.08

19

0.64

`\mu` =

`\sigma^2` =

`\sigma` =

What is the expected value of `X`?

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