SAT Probability and conditional probability Practice Question 6 (Hard)

Question bank / Probability and conditional probability

Math · Problem-Solving and Data AnalysisHard

	Defective	Not defective	Total
Machine A	36	1,164	1,200
Machine B	40	760	800
Total	76	1,924	2,000

A factory has two machines. The table summarizes the items produced by each machine in one day and whether each item was defective. If an item produced that day is selected at random from the defective items, what is the probability that it was produced by machine B?

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Answer: 10/19

The condition limits the selection to the defective items: $36 + 40 = 76$ . Of these, $40$ were produced by machine B. The probability is $\frac{40}{76} = \frac{10}{19}$ , or about $0.5263$ .

Using $\frac{40}{800} = 0.05$ finds the probability that a machine B item is defective, which reverses the condition.

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