SAT Probability and conditional probability Practice Question 2 (Hard)

Question bank / Probability and conditional probability

Math · Problem-Solving and Data AnalysisHard

	Online	In person	Total
Grade 10	48	72	120
Grade 11	105	75	180
Total	153	147	300

The table summarizes the results of a survey of $300$ students in which each student chose a preferred class format. If one of the students who prefer online classes is selected at random, what is the probability that the student is in grade $11$ ?

$\frac{7}{20}$

$\frac{7}{12}$

$\frac{35}{51}$

$\frac{51}{100}$

Show answer and explanation

Answer: C

The condition "prefers online" restricts the group to the online column, which has $48 + 105 = 153$ students. Of those, $105$ are in grade $11$ . The probability is $\frac{105}{153} = \frac{35}{51}$ .

Choice B is $\frac{105}{180}$ , the probability that a grade $11$ student prefers online, which reverses the condition.

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