Study on the flySATMathProbability and conditional probability
Math
Probability and conditional probability questions often come with a two-way table or a description of counts sorted into categories.
A simple probability is a favorable count divided by the total, and because the probabilities of all categories add to one, a missing category can be found by subtraction. Conditional probability narrows the total to a single group: the probability that a person prefers tea, given that the person is an adult, uses only the adults as the denominator.
Using the grand total when a row or column total is needed is the most frequent error. Some items work backward, turning a stated probability and a total into a count.
Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.
Question 1Mid
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?
Answer: B — 126
The probability that a book is reference is . Therefore, of the new books are reference books.
Question 2Mid
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 times the number of child tickets sold. How many child tickets were sold?
Answer: C — 120
Student and child tickets account for of the total, or tickets. Their counts are in the ratio , so the number of child tickets is .
Question 3Mid
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?
Answer: A — 225
A proportion of of the packages went to the east or west hub, so this group contains 360 packages. Of those, were routed to the east hub.
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