20% of the items reaching an inspector are defective. The inspector flags 90% of the defective items, and also wrongly flags 5% of the good ones. An item is not flagged. What is the probability that it is defective?

\frac{1}{39}

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\frac{1}{10}

Correct answerYour answer

\frac{1}{5}

Correct answerYour answer

\frac{39}{50}

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CorrectNot quiteAnswer A

Correct answer: A

Not flagged: defective $0.2 \times 0.1 = 0.02$ and good $0.8 \times 0.95 = 0.76$ , in all $0.78$ .
$\frac{0.02}{0.78} = \frac{1}{39}$ .

Worth noting

$\frac{1}{10}$ is the chance that a defective item escapes, not the chance that an unflagged item is defective.

Ten questions from Conditional Probability & Bayes' Theorem, at your own pace.

Explanation