SAT Probability and conditional probability Practice Question 14 (Hard)

Question bank / Probability and conditional probability

Math · Problem-Solving and Data AnalysisHard

	Tested positive	Tested negative	Total
Has condition	45	5	50
Does not have condition	95	855	950
Total	140	860	1,000

The table shows the results of a screening test given to $1{,}000$ people, some of whom had a certain condition. If a person who tested positive is selected at random, what is the probability that the person has the condition?

$\frac{9}{10}$

$\frac{9}{200}$

$\frac{9}{28}$

$\frac{7}{50}$

Show answer and explanation

Answer: C

The condition "tested positive" restricts the group to the $45 + 95 = 140$ people with positive results. Of these, $45$ have the condition. The probability is $\frac{45}{140} = \frac{9}{28}$ .

Choice A is $\frac{45}{50}$ , the probability that a person with the condition tests positive, which reverses the condition.

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