SAT Probability and conditional probability Practice Question 11 (Medium)

Question bank / Probability and conditional probability

Math · Problem-Solving and Data AnalysisMedium

	Sports	Arts	None	Total
Grade 9	30	18	12	60
Grade 10	24	27	9	60
Total	54	45	21	120

The table shows the after-school activities of $120$ students in grades $9$ and $10$ . Each student chose exactly one category. If a grade $10$ student from this group is selected at random, what is the probability that the student participates in arts?

$\frac{9}{20}$

$\frac{3}{5}$

$\frac{9}{40}$

$\frac{3}{8}$

Show answer and explanation

Answer: A

Restrict attention to the $60$ grade $10$ students. Of them, $27$ participate in arts. The probability is $\frac{27}{60} = \frac{9}{20}$ .

Choice B is $\frac{27}{45}$ , the probability that an arts student is in grade $10$ , which reverses the condition.

Ask Owl about this question Next question

Got it wrong? On SAT Owl, Owl looks at the answer you chose and explains the exact mistake, then gives you similar questions until it sticks. Get your predicted SAT score free.