SAT Probability and conditional probability Practice Question 5 (Medium)

Question bank / Probability and conditional probability

Math · Problem-Solving and Data AnalysisMedium

In a class of $30$ students, $18$ play a sport, $12$ play a musical instrument, and $7$ do both. If one student from the class is selected at random, what is the probability that the student does neither?

$\frac{1}{30}$

$\frac{1}{6}$

$\frac{7}{30}$

$\frac{23}{30}$

Show answer and explanation

Answer: C

The number of students who do at least one activity is $18 + 12 - 7 = 23$ , since the $7$ who do both were counted twice. So $30 - 23 = 7$ students do neither. The probability is $\frac{7}{30}$ .

Choice D is the probability that a student does at least one of the activities, which is the complement of the event asked about.

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