Biostatistics: multiplication rule of probability: practice question

A PSM question in the style of the NEET PG paper. Answer it first, then read why the right option is right and why each of the others is wrong.

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PSM · Biostatistics: multiplication rule of probability

Sample item

A healthy person is tested with two independent screening tests, each with a false-positive rate of 10%. What is the probability that this person is falsely positive on both tests?

Original practice item, not a recalled exam question. Nothing here is recorded.

The answer and the reasoning

A. 0.01

For independent events, the probability of both occurring is the product of their separate probabilities, 0.10 multiplied by 0.10, which is 0.01. This is why requiring two positive tests reduces false positives. Adding the probabilities, 0.20, would be the wrong rule.

Option by option

  • A. 0.01 (correct)

    Correct. Independent probabilities multiply, giving 0.01.

  • B. 0.20

    This adds the two probabilities, which is not the rule for both events together.

  • C. 0.19

    This is the probability of at least one false positive, 0.10 plus 0.10 minus 0.01.

  • D. 0.10

    This is the probability of a false positive on one test only.

Source note: Original NextPrep sample item — pending expert review. This item is original practice material awaiting independent expert review, so confirm important facts in a standard textbook.

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Questions about this PSM question

What is the answer to this PSM question?

The best answer is A, 0.01. For independent events, the probability of both occurring is the product of their separate probabilities, 0.

Why is "0.20" not the answer?

This adds the two probabilities, which is not the rule for both events together.

Why is "0.19" not the answer?

This is the probability of at least one false positive, 0.10 plus 0.10 minus 0.01.

Why is "0.10" not the answer?

This is the probability of a false positive on one test only.

What concept does this question test?

It tests Biostatistics: multiplication rule of probability in PSM. 10 multiplied by 0.10, which is 0.01. This is why requiring two positive tests reduces false positives. Adding the probabilities, 0.20, would be the wrong rule.

How hard is this question?

We tag it as an application question: it asks you to use a fact on a patient or a finding. The tag is our own editorial judgement, not an official difficulty rating, so read the reason for every option, not only the answer.

How should I study Biostatistics: multiplication rule of probability?

Practise biostatistics with small calculations until sensitivity, predictive values and risk measures are automatic. Then use the flashcards and the other PSM questions on this site to test what stuck.

Is this a real NEET PG question?

No. It is an original practice item (editorial status: sample, version 1). NextPrep does not publish recalled or leaked questions, and independent faculty review of this item has not been completed yet, so confirm important facts in a standard textbook.