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------------------------------------------------ In a rolling mill, ironworks rails are manufactured. Defects of a certain kind can occur on the rail pieces. The number of defects per rail piece is Poisson distributed with a mean value of 0.1. If a piece of rail has at least one defect, it is discarded.

Calculate the probability that a piece of rail will be discarded. Answer with at least three decimal places.

To calculate the probability that a piece of rail will be discarded, we need to calculate the probability of having at least one defect. In this case, the waiting value (λ) is 0.1, which represents the average number of defects per rail piece.

The probability of having at least one defect in a Poisson distribution with a waiting value of λ is given by 1 - e^(-λ).

Substituting the value of λ = 0.1 into the formula, we get:

Probability of having at least one defect = 1 - e^(-0.1)

Using a calculator, we can evaluate this expression to get the probability:

Probability of having at least one defect ≈ 0.095

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