Question

new spark plugs have just been installed in a small airplane with a two-cylinder engine. for each spark plug, the probability that it is defective and will fail during its first 20 minutes of flight is 1/2,000, independent of the other spark plugs.(a) for any given spark plug, what is the probability that it will not fail during the first 20 minutes of flight? (round your answer to four decimal places.)0.9995 correct: your answer is correct.(b) what is the probability that none of the two spark plugs will fail during the first 20 minutes of flight? (round your answer to four decimal places.)0.0010 incorrect: your answer is incorrect.(c) what is the probability that at least one of the spark plugs will fail? (round your answer to four decimal places.)

Answer 1

Using the binomial distribution, the probabilities are given as follows:

a) Any spark plug not failing during the flight: 0.9995.

b) None of the two failing during the flight: 0.9990.

c) At least one of the two failing during the flight: 0.0010.

Binomial distribution

The mass function of the binomial probability distribution is given as follows:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In which the parameters are as follows:

• n is the number of trials of the experiment.

• p is the probability of a success on a single trial of the experiment.

The values of these parameters are given as follows:

p = 1/2000 = 0.0005, n = 2.

Hence the probability that a single spark plug will not fail is given as follows:

1 - 0.0005 = 0.9995.

The probability that none fail is:

P(X = 0) = (0.9995)² = 0.9990.

The probability that at least one fails is given as follows:

1 - 0.9990 = 0.0010.

More can be learned about the binomial distribution at https://brainly.com/question/24756209

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