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4/30/2016

 


 

Unit VI Homework?Danyell Marchant

 


 

Student: Danyell Marchant

 

Date: 4/30/16

 


 

Instructor: Tech Support, Kelly Holt,

 

Elizabeth Legault, Jennifer Byrom, Dee

 

Assignment: Unit VI Homework

 

Wessler, Mark Nelson

 

Course: MAT1301?14B?5B16?S1 (1)

 


 

1. Write the event as a set of outcomes. If the event is large, you may describe the event without writing it out.

 

A family has two children and there are less (g)irls than (b)oys.

 

Choose the correct answer below.

 

A. bb, bg, gb, gg

 

B. gg

 

C. bb

 

D. bg, gb

 

2.

 


 

Write the event, "Red appears at least once when we spin the given spinner

 

three times" as a set of outcomes. Abbreviate "red" as "r," "blue" as "b," and

 

"yellow" as "y."

 


 

Of the following sets, which represents the event "Red appears at least once when we spin the given spinner

 

three times"?

 

A. {rrb,rry,rbr,ryr,brr,yrr}

 

B. {rbb,rby,ryb,ryy,brb,bry,bbr,byr,yrb,yry,ybr,yyr,rrb,rry,rbr,ryr,brr,yrr,rrr}

 

C. {rrr,rrb,rry,rbr,ryr,brr,yrr}

 

D. {rbb,rby,ryb,ryy,brb,bry,bbr,byr,yrb,yry,ybr,yyr}

 


 

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3. We are flipping three coins. Outcomes in the sample space are represented by strings of Hs and Ts such as

 

TTH and HHT.

 

a. How many elements are in this sample space?

 

b. Express the event "there are more tails than heads " as a set.

 

c. What is the probability that there are more tails than heads ?

 

d. What is the probability that there are an equal number of tails and heads ?

 

a. There are

 


 

elements in this sample space.

 


 

b. Express the event "there are more tails than heads " as a set. Choose the correct answer below.

 

A. {TTT, TTH, THT, HTT }

 

B. {TTH, THT, HTT }

 

C. {TTH, HHT, THT, HTT }

 

D. {THT, HTH, HTT, THH }

 

c. The probability that there are more tails than heads is

 


 

. (Simplify your answer.)

 


 

d. The probability that there are an equal number of tails and heads is

 

(Simplify your answer.)

 


 

.

 


 

4. A pair of fair dice is rolled.

 

a. What is the probability of rolling a sum of 3?

 

b. What are the odds against rolling a sum of 3?

 

a. The probability of rolling a sum of 3 is

 


 

1

 

18

 


 

. (Simplify your answer.)

 


 

b. What are the odds against rolling a sum of 3?

 

A. 17 to 18

 

B. 51 to 1

 

C. 17 to 1

 

D. 1 to 17

 


 

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5. One card is selected randomly from a standard 52?card deck.

 

a. What is the probability of drawing a spade?

 

b. What are the odds against drawing a spade?

 

1

 


 

Click the icon to view a diagram of a standard 52?card deck.

 

1

 


 

a. The probability of drawing a spade is

 


 

4

 


 

. (Simplify your answer.)

 


 

b. What are the odds against drawing a spade?

 

A. 1 to 13

 

B. 3 to 1

 

C. 1 to 4

 

D. 1 to 3

 


 

1: Standard 52?card deck

 


 

YOU ANSWERED:

 


 

4

 


 

13

 


 

6. Suppose that 3 cards are drawn from a well?shuffled deck of 52 cards. What is the probability that all 3 are black ?

 

The probability is

 

.117647

 

.

 

(Round to six decimal places as needed.)

 

7. If the odds against event E are 7 to 3, what is the probability of E?

 

The probability of event E is

 


 

3

 


 

.

 


 

10

 


 

(Simplify your answer.)

 

8. If P(E) = 0.3, what are the odds against E?

 

The odds against E are

 

(Simplify your answers.)

 


 

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9. If the odds against a particular soccer team winning a soccer tournament are 7 to 3, what is the probability that

 

they will win the tournament?

 

Identify the problem solving method that should be used. Choose the correct answer below.

 

A. The Analogies Principle

 

B. The Choose Good Names for Unknown Strategies Principle

 

C. The Be Systematic Principle

 

D. The Draw Pictures Principle

 

The probability that the soccer team will win the tournament is

 

(Simplify your answer.)

 


 

.

 


 

10. One parent who is a carrier and one parent who has sickle-cell anemia have a child. Construct a Punnett square

 

and find the probability that the child is normal. A person with two sickle?cell genes will have the disease, a

 

person with only one sickle?cell gene will be a carrier of the disease, and a person with no sickle?cell genes will be

 

normal. Denote the sickle?cell gene by s and the normal gene by n. Use lowercase letters to indicate that neither

 

s nor n is dominant.

 

Complete the Punnett square below.

 

Second Parent

 

n

 

First

 

Parent s

 


 

s

 


 

s

 


 

ns

 


 

ns

 


 

carrier

 


 

carrier

 


 

ss

 

has the disease

 


 

ss

 

has the disease

 


 

The probability that the child is normal is

 

(Simplify your answer.)

 

YOU ANSWERED:

 


 

0

 


 

.

 


 

1

 


 

2

 


 

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11. Cystic fibrosis is a serious inherited lung disorder that often causes death in victims during early childhood.

 

Because the gene for this disease is recessive, two apparently healthy adults, called carriers, can have a child

 

with the disease. We will denote the normal gene by N and the cystic fibrosis gene by c to indicate its recessive

 

nature.

 

a. Construct a Punnett square to describe the genetic possibilities for a child

 

?

 

whose two parents ?

 

are carriers of cystic fibrosis.

 

b. What is the probability that this child will be a carrier of cystic fibrosis ?

 

a. Complete the Punnett square below.

 

Second Parent

 

c

 

First

 

Parent N

 


 

c

 


 

N

 


 

cc

 


 

cN

 


 

has disease

 


 

carrier

 


 

Nc

 

carrier

 


 

NN

 

normal

 

1

 


 

b. The probability that the child will be a carrier of cystic fibrosis is

 


 

.

 


 

2

 


 

(Simplify your answer.)

 


 

12. A hamburger franchise is giving away a batch of scratch?and?win tickets with the chance to win an order of french

 

fries. There is a 1 in 10 chance that you win an order of french fries.

 

What is the probability that you do not win an order of french fries?

 

9

 


 

The probability you will not win an order of french fries is

 


 

.

 


 

10

 


 

(Type an integer or simplified fraction.)

 

13. A pair of dice is rolled. What is the probability of getting a sum less than 3?

 

What is the probability of getting a sum less than 3?

 


 

1

 

36

 


 


 


 

(Type an integer or simplified fraction.)

 

14. If eleven coins are flipped, what is the probability of obtaining at least one head?

 

P(obtaining at least one head) =

 


 

2047

 

2048

 


 

. (Type an integer or a simplified fraction.)

 


 

15. What is the probability of getting either a heart or a queen when drawing a single card from a deck of 52 cards?

 

What is the probability that the card is either a heart or a queen ?

 


 

4

 

13

 


 


 


 

(Simplify your answer. Type a fraction.)

 


 

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16. Assume that A and B are events. If P(A? B) = 0.6 , P(A) = 0.4 , and P(B) = 0.45 , find P(A? B).

 

P(A? B) =

 

.25

 

(Simplify your answer. Type an integer or a decimal.)

 

17. If P(A? B) = 0.8 , P(A) = 0.5 , and P(A? B) = 0.25 , find P(B). Assume that A and B are events.

 

P(B) =

 

(Simplify your answer. Type an integer or a decimal.)

 

18.

 


 

An employee at an electronics store earns both a salary and a

 

monthly commission as a sales representative. The following table

 

lists her estimates of the probabilities of earning various

 

commissions next month. What is the probability that the sales

 

representative will earn at least $1,000?

 


 

Commission

 

Less than $1,000

 

$1,000 $1,249

 

$1,250 $1,499

 

$1,500 $1,749

 

$1,750 $1,999

 

$2,000 $2,249

 

$2,250 $2,499

 

$2,500 or more

 


 

?

 

?

 

?

 

?

 

?

 

?

 


 

Probability

 

0.06

 

0.14

 

0.24

 

0.34

 

0.14

 

0.04

 

0.01

 

0.03

 


 

P(sales representative will earn at least $1,000 in commissions) =

 

.94

 

(Type an integer or decimal rounded to two decimal places as needed.)

 

19. A college administration has conducted a study of 169 randomly selected students to determine the relationship

 

between satisfaction with academic advisement and academic success. They obtained the following information:

 

Of the 75 students on academic probation, 42 are not satisfied with advisement? however, only 16 of the students

 

not on academic probation are dissatisfied with advisement. What is the probability that a student selected at

 

random is not on academic probation and is not satisfied with advisement?

 

The probability is

 


 

. (Round to two decimal places as needed.)

 


 

20. Assume that two fair dice are rolled. First compute P(F) and then P(F|E). Explain why one would expect the

 

probability of F to change as it did when we added the condition that E had occurred.

 

F: the total is five

 


 

E: an odd total shows on the dice

 


 

Compute P(F).

 

P(F) =

 


 

4

 

9

 


 

(Simplify your answer.)

 


 

Compute P(F|E).

 

P(F|E) =

 


 

(Simplify your answer.)

 


 

Why does the probability of F change?

 

A. The event E doubles the number of the possible outcomes, decreasing the probability.

 

B. The event E halves the number of the possible outcomes, increasing the probability.

 

C. The event E halves the number of the possible outcomes, decreasing the probability.

 

D. The event E doubles the number of the possible outcomes, increasing the probability.

 

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21. We are drawing a single card from a standard 52?card deck. Find the following probability.

 

P(two | nonface card)

 

The probability is

 


 

1

 

13

 


 

. (Type an integer or a simplified fraction.)

 


 

22. Assume that 2 cards are drawn from a standard 52?card deck. Find the following probabilities.

 

a) Assume the cards are drawn without replacement. Find the probability of drawing 2 face cards.

 

b) Assume the cards are drawn with replacement. Find the probability of drawing 2 face cards.

 

a. The probability of drawing 2 face cards without replacement is

 

(Simplify your answer.)

 


 

.

 


 

b. The probability of drawing 2 face cards with replacement is

 

(Simplify your answer.)

 


 

.

 


 

23. Assume that 2 cards are drawn from a standard 52?card deck. Find the following probabilities.

 

a) Assume the cards are drawn without replacement. Find the probability of drawing a non-red card followed by

 

a red card.

 

b) Assume the cards are drawn with replacement. Find the probability of drawing a non-red card followed by

 

a red card.

 

a. The probability of drawing a non-red card followed by a red card without replacement is

 

(Simplify your answer.)

 

b. The probability of drawing a non-red card followed by a red card with replacement is

 

(Simplify your answer.)

 


 

.

 


 

.

 


 

24. We are drawing two cards without replacement from a standard 52?card deck. Find the probability that we draw at

 

least one black card.

 

The probability is

 


 

. (Type an integer or a simplified fraction.)

 


 

25. A pair of dice is rolled ten times. Find the probability of rolling an even total exactly once.

 

The probability that an even total is rolled exactly once is

 

(Round to three decimal places as needed.)

 


 

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26. Find the probability, P(Q? R), associated with the tree

 

diagram.

 


 

0.7

 


 

What is P(Q? R)?

 


 

R

 

0.3

 


 

S

 

0.2

 


 

(Round to the nearest hundredth.)

 


 

0.2

 


 

M

 


 

R

 


 

0.5

 

N

 


 

0.8

 


 

S

 

Q

 


 

0.3

 

0.8

 

R

 

S

 


 

0.2

 


 

27. An experiment and two events are given. Determine if the events are independent or dependent.

 

Experiment: A penny and a nickel are flipped.

 

Event A: Tails on the nickel.

 

Event B: Heads on the nickel.

 

The two events A and B are (1)

 


 

(1)

 


 

dependent.

 

independent.

 


 

28. Imagine a subject is taking part in a study to test a new cold medicine. The probability that the subject is taking

 

drug A is 30%, that it is drug B is 40%, and that it is drug C is 30%. From past clinical trials, the probabilities that

 

these drugs will improve his condition are A (30%), B (30%), and C (60%). What is the probability that he will

 

improve?

 

The probability is

 

(Type an integer or decimal)

 


 

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