Etext Week4 Res/342

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5.62 A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully.

The probability of one alternator failing is .02. The probability that neither would fail is .98 due to the outcomes of probabilities totaling 1.00.

The alternators are named Z and Y, if the probability of alternator Z failing on the one hour flight is .02. The same can be said for alternator Y, therefore the probability of alternator Y failing is .02. The probability that both alternators will fail should be the outcome of the probability of each alternator failing multiplied by the other.

P(Both Alt)= P(Z) x P(Y)

P(Both Alt)= (.02) x (.02)

P(Both Alt)= .0004

To find the probability of both alternators working without failure for the one-hour flight, we have to multiply the probability of each alternator working without failure.

P(Both Alt)= P(Z) x P(Y)

P(Both Alt)= .98 x .98

P(Both Alt)= .9604

The probability that alternator Z works without failure and alternator Y fails, so the next step would be to multiply the probability Z works and the probability that Y fails.

P(Z fail, Y work)= P(Z fail) x P(Y work)

P(Z fail, Y work)= .02 x .98

P(Z fail, Y work)= .0196

We need to do the following to figure out the probability that one or the other will fail.

P(Z fail, Y work)= P(Z fail, Y work) + P(Z fail, Y work)

P(Z fail, Y work)= .0196 + .0196

P(Z fail, Y work)= .0392

Therefore, these are the results for a, b, and c:

(a) .0004 (b) .9604 (c) .0392

5.70 The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime? Explain your reasoning carefully. Hint: Assume independent...