25 hard SAT Probability & conditional probability questions

A box contains 120 marbles. Each marble is either red or blue and either large or small. There are 50 red marbles, of which 18 are large. There are 35 large marbles in total. What is the probability that a randomly selected marble is blue and small?

• A$\displaystyle \frac{67}{120}$
• B$\displaystyle \frac{53}{120}$
• C$\displaystyle \frac{85}{120}$
• D$\displaystyle \frac{53}{85}$

The table summarizes the distribution of major and class year for 120 students at a university. One of these students will be selected at random. What is the probability of selecting a junior, given that the student is a mathematics major? | | Sophomore | Junior | Senior | Total | |-----------|-----------|--------|--------|-------| | Biology | 15 | 12 | 13 | 40 | | Mathematics| 8 | 18 | 14 | 40 | | Physics | 17 | 10 | 13 | 40 | | Total | 40 | 40 | 40 | 120 |

• A$\displaystyle \frac{1}{3}$
• B$\displaystyle \frac{18}{120}$
• C$\displaystyle \frac{9}{20}$
• D$\displaystyle \frac{29}{60}$

What fraction of the employees who work in the sales department have been with the company for more than 10 years?

• A$\displaystyle \frac{1}{4}$
• B$\displaystyle \frac{3}{20}$
• C$\displaystyle \frac{3}{5}$
• D$\displaystyle \frac{3}{4}$

A spinner is divided into 8 equal sections numbered 1 through 8. The spinner is spun twice. What is the probability that at least one of the two spins results in a number greater than 5?

• A$\displaystyle \frac{3}{8}$
• B$\displaystyle \frac{6}{16}$
• C$\displaystyle \frac{9}{16}$
• D$\displaystyle \frac{39}{64}$

A bag contains 15 red marbles, 20 blue marbles, and 25 green marbles. A marble is selected at random from the bag and not replaced. Then a second marble is selected at random from the bag. What is the probability that both marbles selected are red?

• A$\displaystyle \frac{1}{4}$
• B$\displaystyle \frac{7}{118}$
• C$\displaystyle \frac{15}{59}$
• D$\displaystyle \frac{1}{16}$

In a survey of 200 employees, 120 employees work in sales and 90 employees have been with the company for more than 5 years. If 60 employees both work in sales and have been with the company for more than 5 years, what is the probability that a randomly selected employee either works in sales or has been with the company for more than 5 years?

• A$\displaystyle \frac{21}{40}$
• B$\displaystyle \frac{3}{4}$
• C$\displaystyle \frac{3}{5}$
• D$\displaystyle \frac{63}{100}$

A bag contains red marbles and blue marbles. The probability of selecting a red marble at random is $\displaystyle \frac{3}{7}$. If there are 12 red marbles in the bag, what is the probability of selecting a blue marble at random?

• A$\displaystyle \frac{3}{7}$
• B$\displaystyle \frac{4}{7}$
• C$\displaystyle \frac{3}{4}$
• D$\displaystyle \frac{7}{12}$

The table summarizes the results of a quality control test for 150 items produced by two machines. One item will be selected at random. What is the probability that the item is defective, given that it was produced by Machine B? | | Defective | Not Defective | Total | |-----------|-----------|---------------|-------| | Machine A | 5 | 70 | 75 | | Machine B | 9 | 66 | 75 | | Total | 14 | 136 | 150 |

• A$\displaystyle \frac{9}{150}$
• B$\displaystyle \frac{14}{150}$
• C$\displaystyle \frac{3}{25}$
• D$\displaystyle \frac{23}{150}$

What fraction of the students who participate in at least one sport play basketball?

• A$\displaystyle \frac{1}{3}$
• B$\displaystyle \frac{2}{5}$
• C$\displaystyle \frac{3}{5}$
• D$\displaystyle \frac{2}{3}$

A bag contains 60 marbles: 15 red, 20 blue, and 25 green. A marble is randomly selected from the bag and not replaced. Then a second marble is randomly selected. What is the probability that both marbles selected are blue?

• A$\displaystyle \frac{1}{3}$
• B$\displaystyle \frac{19}{177}$
• C$\displaystyle \frac{2}{9}$
• D$\displaystyle \frac{40}{120}$

A box contains 8 white cards, 12 black cards, and 10 gray cards. Two cards are selected at random from the box without replacement. What is the probability that the first card is white and the second card is black?

• A$\displaystyle \frac{4}{15}$
• B$\displaystyle \frac{4}{29}$
• C$\displaystyle \frac{16}{145}$
• D$\displaystyle \frac{1}{5}$

A box contains red marbles and blue marbles. The probability of randomly selecting a red marble is $\displaystyle \frac{7}{12}$. If there are 35 red marbles in the box, what is the probability of selecting a blue marble?

• A$\displaystyle \frac{5}{7}$
• B$\displaystyle \frac{5}{12}$
• C$\displaystyle \frac{7}{12}$
• D$\displaystyle \frac{12}{35}$

The table summarizes the distribution of employment status and education level for 150 adults in a survey.   High School College Graduate School Total Employed 28 42 35 105 Unemployed 12 18 15 45 Total 40 60 50 150 One of these adults will be selected at random. What is the probability of selecting an employed adult, given that the adult has a College or Graduate School education?

• A$\displaystyle \frac{77}{150}$
• B$\displaystyle \frac{77}{105}$
• C$\displaystyle \frac{7}{10}$
• D$\displaystyle \frac{105}{110}$

A box contains 60 marbles. Of these marbles, 24 are red, 18 are blue, and the rest are green. Of the red marbles, 9 are large and the rest are small. Of the blue marbles, 6 are large and the rest are small. Of the green marbles, 3 are large and the rest are small. One marble will be selected at random from the box. What is the probability that the selected marble is large, given that it is red or blue?

• A$\displaystyle \frac{15}{60}$
• B$\displaystyle \frac{5}{14}$
• C$\displaystyle \frac{1}{4}$
• D$\displaystyle \frac{33}{60}$

A student takes a two-part quiz. The probability that the student answers the first question correctly is 0.6. If the student answers the first question correctly, the probability of answering the second question correctly is 0.9. If the student answers the first question incorrectly, the probability of answering the second question correctly is 0.3. What is the probability that the student answers both questions correctly?

• A$0.42$
• B$0.54$
• C$0.72$
• D$0.9$

A company has 300 employees. Of these, 180 have a college degree, 150 have more than 5 years of experience, and 90 have both a college degree and more than 5 years of experience. If an employee with more than 5 years of experience is selected at random, what is the probability that the employee has a college degree?

• A$\displaystyle \frac{3}{10}$
• B$\displaystyle \frac{3}{5}$
• C$\displaystyle \frac{90}{180}$
• D$\displaystyle \frac{240}{300}$

A deck contains cards numbered 1 through 50. The probability of drawing a card with a number that is a multiple of 8 is $\displaystyle \frac{k}{50}$. What is the probability of drawing a card with a number that is NOT a multiple of 8?

• A$\displaystyle \frac{44}{50}$
• B$\displaystyle \frac{6}{50}$
• C$\displaystyle \frac{44}{44}$
• D$\displaystyle \frac{25}{50}$

The table summarizes the results of a quality control inspection of 300 manufactured parts.   Pass Fail Total Machine X 85 15 100 Machine Y 110 40 150 Machine Z 45 5 50 Total 240 60 300 One of these parts will be selected at random. What is the probability of selecting a part that passed inspection, given that it was produced by Machine X or Machine Y?

• A$\displaystyle \frac{195}{300}$
• B$\displaystyle \frac{195}{240}$
• C$\displaystyle \frac{39}{50}$
• D$\displaystyle \frac{240}{250}$

A conference has 320 attendees classified by profession and registration type. Of these attendees, 120 are engineers, 100 are scientists, and 100 are educators. Of the engineers, 80 registered early and 40 registered late. Of the scientists, 60 registered early and 40 registered late. Of the educators, 50 registered early and 50 registered late. One attendee will be selected at random. What is the probability that the selected attendee is a scientist, given that the attendee registered early?

• A$\displaystyle \frac{3}{16}$
• B$\displaystyle \frac{6}{19}$
• C$\displaystyle \frac{5}{16}$
• D$\displaystyle \frac{1}{3}$

A jar contains 120 marbles: 45 red, 35 blue, and 40 green. A marble is selected at random from the jar and not replaced. Then a second marble is selected at random. What is the probability that both marbles selected are red?

• A$\displaystyle \frac{9}{32}$
• B$\displaystyle \frac{33}{238}$
• C$\displaystyle \frac{45}{120}$
• D$\displaystyle \frac{9}{64}$

At a school fundraiser, 65 percent of the attendees purchased raffle tickets and 40 percent of the attendees purchased both raffle tickets and auction items. An attendee will be selected at random. What is the probability that the attendee purchased auction items, given that the attendee purchased raffle tickets?

• A$\displaystyle \frac{8}{13}$
• B$\displaystyle \frac{2}{5}$
• C$\displaystyle \frac{8}{21}$
• D$\displaystyle \frac{21}{20}$

The table summarizes the distribution of major and class year for 200 students at a university.   Freshman Sophomore Junior Senior Total Engineering 18 22 15 25 80 Business 12 16 18 14 60 Liberal Arts 20 18 12 10 60 Total 50 56 45 49 200 One of these students will be selected at random. What is the probability of selecting an Engineering major, given that the student is a Junior or Senior?

• A$\displaystyle \frac{40}{94}$
• B$\displaystyle \frac{40}{200}$
• C$\displaystyle \frac{80}{94}$
• D$\displaystyle \frac{40}{80}$

A library has 240 books classified by genre and availability. Of these books, 100 are fiction, 80 are nonfiction, and 60 are reference. Of the fiction books, 70 are available and 30 are checked out. Of the nonfiction books, 50 are available and 30 are checked out. Of the reference books, 40 are available and 20 are checked out. One book will be selected at random. What is the probability that the selected book is fiction, given that it is available?

• A$\displaystyle \frac{7}{16}$
• B$\displaystyle \frac{5}{12}$
• C$\displaystyle \frac{7}{24}$
• D$\displaystyle \frac{100}{240}$

A quality control inspector examines a batch of products in two stages. In the first stage, each product has a probability of 0.8 of passing inspection. If a product passes the first stage, it moves to the second stage, where it has a probability of 0.7 of passing. What is the probability that a randomly selected product passes both stages of inspection?

• A$0.56$
• B$0.75$
• C$0.8$
• D$1.5$

A box contains tiles numbered 1 through 20. If two tiles are drawn without replacement, what is the probability that both tiles show even numbers?

• A$\displaystyle \frac{9}{38}$
• B$\displaystyle \frac{1}{4}$
• C$\displaystyle \frac{1}{2}$
• D$\displaystyle \frac{10}{19}$