A candidate clears the first round of a selection with probability 0.8. Having cleared it, the candidate clears the second round with probability 0.6, and having cleared both, the third round with probability 0.75. What is the probability that the candidate clears the first two rounds but not the third?

0.12

Correct answerYour answer

0.25

Correct answerYour answer

0.36

Correct answerYour answer

0.48

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Once the first two rounds are cleared, the third is missed with probability $1 - 0.75 = 0.25$ .
$0.8 \times 0.6 \times 0.25 = 0.12$ .

Worth noting

0.25 is the chance of missing the third round once the first two are cleared; the candidate must first clear them, with probability $0.8 \times 0.6$ .

Concept: The multiplication theorem for three draws or stages
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsThe multiplication theorem

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

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