20 medium SAT Probability & conditional probability questions

A box contains 120 marbles. Each marble is either glass or plastic, and each marble is either large or small. There are 48 glass marbles, of which 18 are large. There are 72 plastic marbles, of which 30 are large. If one marble is selected at random from the box, what is the probability of selecting a small plastic marble?

• A$\displaystyle \frac{42}{120}$
• B$\displaystyle \frac{30}{120}$
• C$\displaystyle \frac{72}{120}$
• D$\displaystyle \frac{60}{120}$

TABLE: A survey of 200 customers at a store categorized by purchase type. Rows: 'Electronics' and 'Clothing'. Columns: 'Used Coupon' and 'No Coupon'. Electronics: Used Coupon 30, No Coupon 70, Total 100. Clothing: Used Coupon 45, No Coupon 55, Total 100. Total: Used Coupon 75, No Coupon 125, Total 200. If one customer is selected at random from those who purchased electronics, what is the probability that the customer used a coupon?

• A$0.15$
• B$0.30$
• C$0.375$
• D$0.40$

What fraction of the employees in the sales department have been with the company for more than 5 years?

• A$\displaystyle \frac{9}{25}$
• B$\displaystyle \frac{3}{5}$
• C$\displaystyle \frac{2}{3}$
• D$\displaystyle \frac{3}{4}$

A jar contains 15 marbles: 5 are green, 6 are blue, and 4 are red. If two marbles are selected at random without replacement, what is the probability that both marbles are blue?

• A$\displaystyle \frac{1}{7}$
• B$\displaystyle \frac{2}{5}$
• C$\displaystyle \frac{12}{225}$
• D$\displaystyle \frac{36}{225}$

The table summarizes the distribution of major and class year for 200 college students. TABLE: Rows are Sophomore/Junior/Senior, Columns are Engineering/Business/Total. Sophomore: 24 Engineering, 36 Business, 60 Total. Junior: 32 Engineering, 28 Business, 60 Total. Senior: 44 Engineering, 36 Business, 80 Total. Column Totals: 100 Engineering, 100 Business, 200 Total. If one of these students is selected at random, what is the probability of selecting a junior given that the student is an engineering major?

• A$\displaystyle \frac{8}{25}$
• B$\displaystyle \frac{3}{10}$
• C$\displaystyle \frac{4}{5}$
• D$\displaystyle \frac{8}{15}$

A survey of 240 students asked whether they prefer tea or coffee. Of the students surveyed, 156 prefer coffee and 84 prefer tea. If one of these students is selected at random, what is the probability of selecting a student who prefers tea?

• A$\displaystyle \frac{7}{20}$
• B$\displaystyle \frac{13}{20}$
• C$\displaystyle \frac{7}{13}$
• D$\displaystyle \frac{1}{3}$

TABLE: A table shows the number of employees at a company by department and work mode. Rows: 'Sales' and 'Marketing'. Columns: 'Remote' and 'In-office'. Sales: Remote 18, In-office 32, Total 50. Marketing: Remote 27, In-office 33, Total 60. Total: Remote 45, In-office 65, Total 110. If one employee from the marketing department is selected at random, what is the probability that the employee works remotely?

• A$0.27$
• B$0.41$
• C$0.45$
• D$0.60$

What fraction of the students enrolled in Spanish classes are also enrolled in an advanced literature course?

• A$\displaystyle \frac{3}{20}$
• B$\displaystyle \frac{9}{40}$
• C$\displaystyle \frac{2}{5}$
• D$\displaystyle \frac{3}{5}$

A bag contains 5 red marbles and 3 blue marbles. A marble is drawn at random, replaced, and then a second marble is drawn at random. What is the probability that both marbles drawn are red?

• A$\displaystyle \frac{5}{16}$
• B$\displaystyle \frac{5}{14}$
• C$\displaystyle \frac{25}{64}$
• D$\displaystyle \frac{5}{8}$

A jar contains 18 red balls and 12 white balls. If one ball is selected at random, replaced, and then a second ball is selected at random, what is the probability that both balls selected are red?

• A$\displaystyle \frac{3}{5}$
• B$\displaystyle \frac{9}{25}$
• C$\displaystyle \frac{6}{25}$
• D$\displaystyle \frac{51}{145}$

A library has 350 books classified by genre and format. Of these books, 140 are fiction and 210 are nonfiction. Among the fiction books, 84 are hardcover. Among the nonfiction books, 105 are hardcover. If one book is selected at random from the library, what is the probability of selecting a paperback fiction book?

• A$\displaystyle \frac{56}{350}$
• B$\displaystyle \frac{84}{350}$
• C$\displaystyle \frac{140}{350}$
• D$\displaystyle \frac{161}{350}$

A survey of 180 students asked whether they prefer online classes, in-person classes, or both. The results are shown in the table.

• A$\displaystyle \frac{65}{180}$
• B$\displaystyle \frac{15}{40}$
• C$\displaystyle \frac{15}{65}$
• D$\displaystyle \frac{25}{180}$

What fraction of the students who play a musical instrument are in the school band?

• A$\displaystyle \frac{1}{4}$
• B$\displaystyle \frac{2}{5}$
• C$\displaystyle \frac{5}{8}$
• D$\displaystyle \frac{4}{5}$

A box contains 120 tokens. Each token is labeled with exactly one letter: A, B, C, or D. There are 36 tokens labeled A, 28 tokens labeled B, and 32 tokens labeled C. If one token is selected at random from the box, what is the probability of selecting a token labeled D?

• A$\displaystyle \frac{1}{4}$
• B$\displaystyle \frac{1}{5}$
• C$\displaystyle \frac{4}{5}$
• D$\displaystyle \frac{2}{5}$

A box contains 15 green marbles, 24 red marbles, and 21 yellow marbles. If one marble is selected at random from the box, what is the probability of selecting a marble that is not yellow?

• A$\displaystyle \frac{7}{20}$
• B$\displaystyle \frac{13}{20}$
• C$\displaystyle \frac{5}{8}$
• D$\displaystyle \frac{13}{21}$

TABLE: A two-way table shows 150 library visitors categorized by age group and borrowing status. Rows: 'Adult' and 'Child'. Columns: 'Borrowed Books' and 'Did Not Borrow'. Adult: Borrowed Books 54, Did Not Borrow 36, Total 90. Child: Borrowed Books 42, Did Not Borrow 18, Total 60. Total: Borrowed Books 96, Did Not Borrow 54, Total 150. If one visitor who borrowed books is selected at random, what is the probability that the visitor is an adult?

• A$0.36$
• B$0.56$
• C$0.60$
• D$0.64$

What fraction of the hardcover books in the fiction section were published after 2010?

• A$\displaystyle \frac{9}{20}$
• B$\displaystyle \frac{2}{3}$
• C$\displaystyle \frac{3}{4}$
• D$\displaystyle \frac{9}{10}$

A deck contains 60 cards. Each card is marked with exactly one symbol: star, circle, or triangle. There are 18 cards with stars and 25 cards with circles. If one card is selected at random from the deck, what is the probability of selecting a card with a triangle?

• A$\displaystyle \frac{17}{60}$
• B$\displaystyle \frac{43}{60}$
• C$\displaystyle \frac{17}{43}$
• D$\displaystyle \frac{7}{12}$

The table shows the distribution of 240 employees at a company by department and employment status.

• A$\displaystyle \frac{50}{170}$
• B$\displaystyle \frac{50}{240}$
• C$\displaystyle \frac{5}{7}$
• D$\displaystyle \frac{70}{240}$

A research study categorized 450 participants by age group and exercise frequency. The results are shown in the table.

• A$\displaystyle \frac{60}{450}$
• B$\displaystyle \frac{60}{150}$
• C$\displaystyle \frac{3}{10}$
• D$\displaystyle \frac{90}{450}$