A certain airplane has two independent alternators to provide electrical power.

Question

A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a one-hour flight is 0.020. rev: 3_21_2013_QC_28514 (a) What is the probability that both will fail? (Round your answer to 4 decimal places.) Probability .0004 (b) What is the probability that neither will fail? (Round your answer to 4 decimal places.) Probability (c) What is the probability that at least one fails? (Round your answer to 4 decimal places.) Probability

Explanation / Answer

(a) What is the probability that both will fail? (Round your answer to 4 decimal places.) Probability .0004

P(both fail) = 0.020*0.020 = 0.0004 [ANSWER]

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(b) What is the probability that neither will fail? (Round your answer to 4 decimal places.) Probability

Note that the probability that each will work is 1 - 0.020 = 0.980.

P(neither fails) = (1-0.020)*(1-0.020) = 0.9604 [ANSWER]

(c) What is the probability that at least one fails? (Round your answer to 4 decimal places.) Probability

P(at least one fails) = 1 - P(neither fails) = 1 - 0.9604 = 0.0396 [ANSWER]

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