A machine runs when its motor works and at least one of its two fans works. The motor and the two fans work independently, with probabilities 0.9, 0.8 and 0.7. What is the probability that the machine runs?

0.504

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0.846

Correct answerYour answer

0.94

Correct answerYour answer

0.994

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CorrectNot quiteAnswer B

Correct answer: B

Both fans fail with probability $0.2 \times 0.3 = 0.06$ , so at least one works with probability $0.94$ .
The motor must work as well: $0.9 \times 0.94 = 0.846$ .

Worth noting

0.504 is $0.9 \times 0.8 \times 0.7$ , which needs both fans, but one is enough.

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

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