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Probability and conditional probability — SAT practice questions

Probability and conditional probability on the SAT Math test asks students to convert given probabilities into counts for items sorted into labeled groups, then find a missing category or a probability restricted to what remains. A student must use that the groups together fill the whole set, turn a probability into a count, and compute a conditional probability after some groups are excluded. Questions are short word problems about books, tickets, or packages; they give probabilities for some groups and ask for a leftover count or a probability among the rest. Answer choices are whole numbers or simplified probabilities, and a common trap is conditioning on the wrong remaining set.

  • Section: Math 44 questions on the paper
  • 102 practice questions in the app

Sample questions

Question 1

A library acquired 525 new books. Each book is classified as fiction, nonfiction, or reference. If one book is selected at random, the probability that it is fiction is 0.36, and the probability that it is nonfiction is 0.40. How many of the new books are classified as reference?

  1. A21
  2. B126
  3. C315
  4. D399
Show answer

Answer: B — 126

The probability that a book is reference is 1−0.36−0.40=0.241-0.36-0.40=0.24. Therefore, 0.24(525)=1260.24(525)=126 of the new books are reference books.

Question 2

A museum sold 800 admission tickets. Each ticket was an adult, senior, student, or child ticket. If one ticket is selected at random, the probability that it is an adult ticket is 0.4125, and the probability that it is a senior ticket is 0.1875. The number of student tickets sold was 53\dfrac{5}{3} times the number of child tickets sold. How many child tickets were sold?

  1. A40
  2. B80
  3. C120
  4. D200
Show answer

Answer: C — 120

Student and child tickets account for 1−0.4125−0.1875=0.41-0.4125-0.1875=0.4 of the total, or 0.4(800)=3200.4(800)=320 tickets. Their counts are in the ratio 5:35:3, so the number of child tickets is 38(320)=120\dfrac{3}{8}(320)=120.

Question 3

A courier service routed 1,000 packages to one of four regional hubs: north, south, east, or west. The probability that a randomly selected package was routed to the north or south hub is 0.64. Among the packages routed to neither the north nor the south hub, the probability that a package was routed to the east hub is 0.625. How many packages were routed to the east hub?

  1. A225
  2. B360
  3. C625
  4. D640
Show answer

Answer: A — 225

A proportion of 1−0.64=0.361-0.64=0.36 of the packages went to the east or west hub, so this group contains 360 packages. Of those, 0.625(360)=2250.625(360)=225 were routed to the east hub.

Practice 102 Probability and conditional probability questions in the app

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