# Probability problem

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The number of failures of a unit from contamination particles on the unit is a Poisson random variable with a mean of 0.02 failures per hour.

a.) What is the probability that the instrument does not fail in an 8-hour shift?

b.) What is the probability of at least one failure in a 24-hour day?

Samples are defective in 1% of cases. Suppose 15 samples are studied, and they can be considered to be independent for being defective. Determine the following probabilities. Use the binomial table to help.

a.) No samples are defective.

b.) At most one sample is defective.

c.) More than half the samples are defective.

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This solution gives the step by step method for computing probability.

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The number of failures of a unit from contamination particles on the unit is a Poisson random variable with a mean of 0.02 failures per hour.

a.) What is the probability that the instrument does not fail in an 8-hour shift?

Let T be the time of first failure. The probability density function of T is given by . This density is said to have the exponential distribution with rate ...

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