# STATS Week 3 Homework 2016

August 31, 2017

Question

1. Determine whether the following statement is true or false. If it is? false, rewrite it as a true statement.

If two events are? independent, P(A|B)equals=?P(B).

2. . A probability experiment consists of rolling a 6-sided die. Find the probability of the event rolling a number less than 4

3. The access code for a car’s security system consists of five digits. The first digit cannot be 2 and the last digit must be odd. How many different codes are available.

4.Determine whether the events E and F are independent or dependent. Justify your answer.

?(a)

?E: A person having a high GPA having a high GPA.

?F: The same person being highly organized being highly organized.

A.

E and F are independent because

being highly organizedbeing highly organized

has no effect on the probability of a person

having a high GPAhaving a high GPA.

B.

E and F are independent because

having a high GPAhaving a high GPA

has no effect on the probability of a person

being highly organizedbeing highly organized.

C.

E and F are dependent because

having a high GPAhaving a high GPA

has no effect on the probability of a person

being highly organizedbeing highly organized.

D.

E and F are dependent because

being highly organizedbeing highly organized

can affect the probability of a person

having a high GPAhaving a high GPA.

5. In the general? population, one woman in eight will develop breast cancer. Research has shown that 1 woman in 600 carries a mutation of the BRCA gene. Eight out of 10 women with this mutation develop breast cancer.

(a) Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene.

The probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene is ….

(Round to one decimal place as? needed.)

6. In a sample of 1000 U.S.? adults, 199 dine out at a restaurant more than once per week. Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S.? adults,

(a) Find the probability that both adults dine out more than once per week.

The probability that both adults dine out more than once per week is ….

(Round to three decimal places as? needed)

7. According to a? survey, 55?% of the residents of a city oppose a downtown casino. Of these 55?% about 66 out of 10 strongly oppose the casino. Complete parts? (a) through? (c).

(a) Find the probability that a randomly selected resident opposes the casino and strongly opposes the casino.

?(b) Find the probability that a randomly selected resident who opposes the casino does not strongly oppose the casino.

?(c) Would it be unusual for a randomly selected resident to oppose the casino and strongly oppose the? casino? Explain.

(a) The probability that a randomly selected resident opposes the casino and strongly opposes the casino is ….

?(Round to three decimal places as? needed.)

8.A standard deck of cards contains 52 cards. One card is selected from the deck.

?(a)

Compute the probability of randomly selecting a five

or eight.

?(b)

Compute the probability of randomly selecting a five

or eight or two.

?(c)

Compute the probability of randomly selecting a seven

or diamond.

? P (five or eight?)equals=

?(Type an integer or a simplified? fraction.)

9.

The percent distribution of live? multiple-delivery births? (three or more? babies) in a particular year for women 15 to 54 years old is shown in the pie chart. Find each probability.

Number of Multiple Births

15-19 1.4%

20-24 6.2%

25-29 21.5%

30-34 37.4%

35-39 24.5%

40-44 5.1%

45-54 3.9%

a. Randomly selecting a mother? 30-39 years old

?P(30 to 39)almost equals?

?(Round to the nearest thousandth as? needed.)

10.Evaluate the given expression and express the result using the usual format for writing numbers? (instead of scientific? notation).

59P2 sidenote: (it looks like 59 to the P power with a 2 maybe times 2?)

11. Outside a? home, there is a 6?-key keypad with letters A, B. C, D, E, F that can be used to open the garage if the correct six?-letter code is entered. Each key may be used only once. How many codes are? possible?

12. A horse race has 10 entries and one person owns 5 of those horses. Assuming that there are no? ties, what is the probability that those five horses finish first comma second comma third comma fourth comma and fifth (regardless of? order)?

?(Round to four decimal places as? needed.)

13. The table below shows the results of a survey in which 141 men and 144 women workers ages 25 to 64 were asked if they have at least one? month’s income set aside for emergencies.

?(a) Find the probability that a randomly selected worker has one? month’s income or more set aside for emergencies.

Men

Women

Total

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Less than one? month’s income

65

83

148

One? month’s income or more

76

61

137

Total

141

144

285

?(a) Find the probability that a randomly selected worker has one? month’s income or more set aside for emergencies.

The probability is

nothing .

?(Round to the nearest thousandth as? needed.)

The table below shows the number of male and female students enrolled in nursing at a particular university for a recent semester.

?(a) Find the probability that a randomly selected student is? male, given that the student is a nursing major.

The table below shows the number of male and female students enrolled in nursing at a particular university for a recent semester.

?14. (a) Find the probability that a randomly selected student is? male, given that the student is a nursing major.

?(b) Find the probability that a randomly selected student is a nursing? major, given that the student is male.

Nursing Majors

?Non-nursing majors

Total

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Males

100

1131

1231

Females

272

1617

2344

Total

827

2748

3575

?(a) Find the probability that a randomly selected student is? male, given that the student is a nursing major.

The probability is

?(Round to three decimal places as? needed.)

.

15.

Use the frequency distribution to the? right, which shows the number of voters? (in millions) according to? age, to find the probability that a voter chosen at random is in the given age range.

not between 18 to 20 years old between 18 to 20 years old

Ages of voters

FrequencyFrequency

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18 to 20

5.35.3

21 to 24

9.49.4

25 to 34

22.322.3

35 to 44

22.622.6

45 to 64

51.151.1

65 and over

29.929.9

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