SAT Probability: Choose the Correct Denominator in a Two-Way Table

A survey records the following students.

If one student is selected at random from those who take art, what is the probability that the student is in grade 11?

Restrict the group first

The student is selected from those who take art. There are 28 such students, so 28 is the denominator.

Count the favorable outcomes

Of the 28 art students, 18 are in grade 11. The probability is 18/28.

Simplify the fraction

Divide numerator and denominator by 2: 18/28 = 9/14.

Ignore the “does not take art” column after applying the condition. In the remaining art column, the grade-11 share is 18 of 18 + 10 students. This immediately gives 18/28 = 9/14.

• 3/10 is 18/60, which selects from all students rather than art students.
• 3/5 is 18/30, the chance of taking art given grade 11. That reverses the condition.
• 7/15 is 28/60, the chance that an unrestricted student takes art.

Using the same table, what is the probability that a randomly selected grade-12 student takes art?

Answer: 1/3

Now the condition is grade 12, so the denominator is 30 and the numerator is 10. Thus 10/30 = 1/3.

If this was difficult, return to probability practice and identify the precise step to improve. These are original PeakSAT teaching examples, not official College Board questions or calibrated score predictions. For official adaptive test practice, use Bluebook (opens in a new tab).