The key idea
“Given that” shrinks the group you choose from. Find the row or column for the condition, then take the part of it that has the other trait. With percents, picture a concrete total like 1,000 and build the counts.
The trap
Dividing by the grand total instead of the total for the condition, or reversing the condition.
Can Desmos do it?
No graphing here: the work is picking the right denominator.
College Board skill: Probability and conditional probability · Problem-Solving and Data Analysis
One question from each level. The drill has 12 at every level, and moves you up after four right in a row.
Level 1 · Warm-up
A survey asked students whether they prefer reading print books or e-books.
Of the juniors, 35 prefer print and 37 prefer e-books. Of the seniors, 40 prefer print and 8 prefer e-books.
If a student who prefers print is chosen at random, what is the probability that the student is a senior?
Show the answer
Answer: 8/15The condition is “prefers print”: 35+40=75 students. Of them, 40 are seniors, so the probability is 7540=158.
Level 2 · Test level
In a group of 180 people, 72 have a library card, and 7 of the people with a library card also have a museum pass. In all, 102 people in the group have a museum pass. If a person who does not have a library card is chosen at random, what is the probability that the person has a museum pass?
Show the answer
Answer: .8796People without a library card: 180−72=108. Museum-pass holders without a library card: 102−7=95. The probability is 10895.
Level 3 · Beyond the test
A company makes 70% of its phones at factory X and the rest at factory Y. Of the phones made at factory X, 1% are defective; of those made at factory Y, 5% are defective. If a defective phone is chosen at random, what is the probability that it was made at factory X?
Show the answer
Answer: 7/22Picture 1,000 phones: 700 from X, of which 7 are defective, and 300 from Y, of which 15 are defective. Of the 22 defective phones, 7 came from X, so the probability is 227.
Practice all 36 questions
Answer in the drill to get instant feedback, climb the levels, and feed your misses into Tailored practice. Free, no account.
Percent change, chained and reversedChained and reversed percent changes, and the right base.36 questions, 3 levelsRates and unit conversionConversion factors, compound units and square units.36 questions, 3 levelsMixtures and concentrationConcentration problems: mixing, adding water, draining and replacing.36 questions, 3 levelsWork ratesJobs done together, fill-and-drain, and late starts.36 questions, 3 levelsMeans, medians, and changes to dataTotals, combined groups and the score you need next.36 questions, 3 levelsRatios and proportionsRatios that change when one part changes.36 questions, 3 levels