Suppose $220$ misprints are distributed randomly throughout a book of $200$ pages. The probability that a given page contains, no misprint is

1. e^{- 02.2}

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1 - e^{- 02.2}

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e^{- 1.1}

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e^{- 2.1}

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Solution

The correct option is C $e^{- 1.1}$
By using Poisson distribution,
$P (x; μ) = \frac{e^{- μ} μ^{x}}{x!}$
$μ$ : The mean number of successes that occur in a specified region(parameter)
x: The actual number of successes that occur in a specified region.
P(x; $μ$ ): The Poisson probability that exactly x successes occur in a Poisson experiment, when the mean number of successes is $μ$
Here, $μ = \frac{220}{200} = 1.1$
$x = 0$ (no misprint)
$P (0; 1.1) = \frac{e^{- 1.1} {1.1}^{0}}{0!} = e^{- 1.1}$

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