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Laabri

PSAT: Problem-Solving & Data Analysis - Probability and conditional probability

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Asemmisa {{asɛmmisaAhyɛnsode}}
1.

The table below shows the number of students from two different high schools who completed summer internships in each of five years.

High school

Year

2008

2009

2010

2011

2012

Foothill

87

80

75

76

70

Valley

44

54

65

76

82

Total

131

134

140

152

152

The table above shows the number of students from two different high schools who completed summer internships in each of five years. No student attended both schools. Of the students who completed a summer internship in 2010, which of the following represents the fraction of students who were from Valley High School?

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2.

There are $n$ nonfiction books and 12 fiction books on a bookshelf. If one of these books is selected at random, what is the probability of selecting a nonfiction book, in terms of $n$?

Asemmisa {{asɛmmisaAhyɛnsode}}
3.

Texting behavior and cell phone use among US teens are summarized in the table below.

Texting behavior

Talks on cell phone daily

Does not talk on cell phone daily

Total

Light

110

146

256

Medium

139

164

303

Heavy

166

74

240

Total

415

384

799

In a study of cell phone use, 799 randomly selected US teens were asked how often they talked on a cell phone and about their texting behavior. The data are summarized in the table above. If one of the 799 teens surveyed is selected at random, what is the probability that the teen talks on a cell phone daily?

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4.

Each vertex of a 14-sided polygon is labeled with one of the 14 letters $A$ through $N$, with a different letter at each vertex. If one vertex is selected at random, what is the probability that the letter $D$ will be at the selected vertex? (Express your answer as a decimal or fraction, not as a percent.)

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5.

A store received a shipment of 1,000 MP3 players, 4 of which were defective. If an MP3 player is randomly selected from this shipment, what is the probability that it is defective?

Asemmisa {{asɛmmisaAhyɛnsode}}
6.

The table below shows the number of people who work in the Human Resources and Accounting departments of a company and the highest level of education they have completed.

Human Resources

Accounting

Bachelor’s degree

4

3

Master’s degree

2

6

A person from one of these departments is to be chosen at random. If the person chosen works in the Human Resources department, what is the probability that the highest level of education the person completed is a master’s degree?

Asemmisa {{asɛmmisaAhyɛnsode}}
7.

The table summarizes the distribution of color and shape for 100 tiles of equal area.

Red

Blue

Yellow

Total

Square

10

20

25

55

Pentagon

20

10

15

45

Total

30

30

40

100

If one of these tiles is selected at random, what is the probability of selecting a red tile? (Express your answer as a decimal or fraction, not as a percent.)

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8.

There are 20 buttons in a bag: 8 white buttons, 2 orange buttons, and 10 brown buttons. If one of these buttons is selected at random, what is the probability of selecting a white button?

Asemmisa {{asɛmmisaAhyɛnsode}}
9.

The table below shows the number of state parks in a certain state that contain camping facilities and bicycle paths.

Has bicycle paths

Does not have bicycle paths

Has camping facilities

20

5

Does not have camping facilities

8

4

If one of these state parks is selected at random, what is the probability that it has camping facilities but does not have bicycle paths?

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10.

Prices of 14 Different Cars

Type of car

Priced at no more than $25,000

Priced greater than $25,000

Total

Nonhybrid

5

3

8

Hybrid

2

4

6

Total

7

7

14

The table above shows information about 14 cars listed for sale on an auto dealership’s website. If one of the cars listed for sale is selected at random, what is the probability that the car selected will be a hybrid car priced at no more than $25,000?

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11.

For a particular machine that produces beads, 29 out of every 100 beads it produces have a defect. A bead produced by the machine will be selected at random. What is the probability of selecting a bead that has a defect?

Asemmisa {{asɛmmisaAhyɛnsode}}
12.

A box contains 13 red pens and 37 blue pens. If one of these pens is selected at random, what is the probability of selecting a red pen? (Express your answer as a decimal or fraction, not as a percent.)

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13.

Each face of a fair 14-sided die is labeled with a number from 1 through 14, with a different number appearing on each face. If the die is rolled one time, what is the probability of rolling a 2?

Asemmisa {{asɛmmisaAhyɛnsode}}
14.

The table below shows the distribution of US states according to whether they have a state-level sales tax and a state-level income tax.

2013 State-Level Taxes

State sales tax

No state sales tax

State income tax

39

4

No state income tax

6

1

To the nearest tenth of a percent, what percent of states with a state-level sales tax do not have a state-level income tax?

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15.

Colors of Marbles in a Bag

Color

Number

Red

8

Blue

10

Green

22

Total

40

The table shows the number of different colors of marbles in a bag. If a marble is chosen at random from the bag, what is the probability that the marble will be blue?

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16.

A band with 45 members has 11 members who play saxophone. If one band member is selected at random, what is the probability of selecting a band member who plays saxophone?

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17.

A survey taken by 1,000 students at a school asked whether they played school sports. The table below summarizes all 1,000 responses from the students surveyed.

Table showing number of males and females who play or do not play a school sport. For playing a school sport: 312 males and 220 females. For not playing a school sport: unknown males and 216 females.

How many of the males surveyed responded that they do not play a school sport?

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18.

Customer Purchases at a Gas Station

Beverage purchased

Beverage not purchased

Total

Gasoline purchased

60

25

85

Gasoline not purchased

35

15

50

Total

90

40

135

On Tuesday, a local gas station had 135 customers. The table above summarizes whether or not the customers on Tuesday purchased gasoline, a beverage, both, or neither. Based on the data in the table, what is the probability that a gas station customer selected at random on that day did not purchase gasoline?

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19.

Question: At a conference, there are a total of 275 attendees. Each attendee is assigned to either group A, group B, or group C. If one of these attendees is selected at random, the probability of selecting an attendee who is assigned to group A is $0.44$ and the probability of selecting an attendee who is assigned to group B is $0.24$. How many attendees are assigned to group C?

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20.

For a science project, Anka recorded whether it rained each weekday and weekend day for 12 weeks. Her results are summarized in the table below.

Weekday and Weekend Day Rain for 12 Weeks

Rain

No rain

Total

Number of weekdays

12

48

60

Number of weekend days

8

16

24

Total

20

64

84

If one of the days on which there was no rain is selected at random, what is the probability the day was a weekend day?

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21.

A data set of three numbers is shown.

$-13, 4, 23$

If a number from this data set is selected at random, what is the probability of selecting a negative number?

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22.

A data set of three numbers is shown.

$-11, -9, 26$

If a number from this data set is selected at random, what is the probability of selecting a positive number?

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23.

On May 10, 2015, there were 83 million Internet subscribers in Nigeria. The major Internet providers were MTN, Globacom, Airtel, Etisalat, and Visafone. By September 30, 2015, the number of Internet subscribers in Nigeria had increased to 97 million. If an Internet subscriber in Nigeria on September 30, 2015, is selected at random, the probability that the person selected was an MTN subscriber is 0.43. There were $p$ million MTN subscribers in Nigeria on September 30, 2015. To the nearest integer, what is the value of $p$?

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24.

A grove has 6 rows of birch trees and 5 rows of maple trees. Each row of birch trees has 8 trees 20 feet or taller and 6 trees shorter than 20 feet. Each row of maple trees has 9 trees 20 feet or taller and 7 trees shorter than 20 feet. A tree from one of these rows will be selected at random. What is the probability of selecting a maple tree, given that the tree is 20 feet or taller?

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25.

Each rock in a collection of 70 rocks was classified as either igneous, metamorphic, or sedimentary, as shown in the frequency table.

Classification

Frequency

igneous

10

metamorphic

33

sedimentary

27

If one of these rocks is selected at random, what is the probability of selecting a rock that is igneous?

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26.

United States Presidents from 1789 to 2015

Table showing ages of United States presidents at first taking office from 1789 to 2015, with intervals 40–44:2, 45–49:7, 50–54:13, 55–59:11, 60–64:7, 65–69:3.

The table above gives the number of United States presidents from 1789 to 2015 whose age at the time they first took office is within the interval listed. Of those presidents who were at least 50 years old when they first took office, what fraction were at least 60 years old?

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27.

The data on the coat color and eye color for 48 Himalayan kittens available for adoption were collected and summarized in the table below.

Table of kittens by coat color and eye color: Cream-tortoiseshell has 16 deep blue, 16 light brown, total 32; Chocolate has 12 deep blue, 4 light brown, total 16; column totals are 28 deep blue, 20 light brown, overall total 48.

What fraction of the chocolate-colored kittens has deep blue eyes?

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28.

A bag contains a total of 60 marbles. A marble is to be chosen at random from the bag. If the probability that a blue marble will be chosen is 0.35, how many marbles in the bag are blue?

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29.

On a street with 7 houses, 2 houses are blue. If a house from this street is selected at random, what is the probability of selecting a house that is blue?

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30.

In a bag, there are 7 red, 4 white, 33 blue, and 33 yellow cubes. If one of these cubes is selected at random, what is the probability of selecting a cube that is neither blue nor yellow?

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31.

Question: At a movie theater, there are a total of 350 customers. Each customer is located in either theater A, theater B, or theater C. If one of these customers is selected at random, the probability of selecting a customer who is located in theater A is $0.48$, and the probability of selecting a customer who is located in theater B is $0.24$. How many customers are located in theater C?

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32.

If 1,200 customers register for new accounts at a social media website every day, what fraction of the first 60,000 new accounts are registered in the first 5 days?

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33.

Of the 8 planets in our solar system, 4 are considered rocky. If a student randomly selects 1 of those 8 planets as a topic for a report, what is the probability that the selected planet will be rocky?