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Luden [163]
3 years ago
5

br%3E%0A%7D%20" id="TexFormula1" title=" \frac{1}{x+1} + \frac{4}{x+4} - \frac{5}{x+5
} " alt=" \frac{1}{x+1} + \frac{4}{x+4} - \frac{5}{x+5
} " align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Anna11 [10]3 years ago
4 0
[ ( x + 4 )( x + 5 ) + 4( x + 1 )( x +  5) - 5( x + 1 )( x + 4 ) ] / [( x + 1 )( x +  4)( x + 5 )] = ( x^2 + 9x + 20 + 4x^2 + 24x +20 - 5x^2 - 25x - 20) / [( x + 1 )( x +  4)( x + 5 )] =
( - 2x + 20 ) /  [( x + 1 )( x +  4)( x + 5 )] = ( - 2)( x - 10) / [( x + 1 )( x +  4)( x + 5 )]
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A levee was designed to protect against floods with an annual exceedance probability of 0.02. A larger flood would cause the lev
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66.76% probability that the levee will NEVER fail in the next 20 years.

Step-by-step explanation:

For each year, there are only two possible outcomes. Either a levee fails during the year, or no levees fail. In each year, the probabilities of levees failing are independent from each other. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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And p is the probability of X happening.

In this problem we have that:

A levee was designed to protect against floods with an annual exceedance probability of 0.02. This means that p = 0.02

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P(X = 0) = C_{20,0}*(0.02)^{0}*.(0.98)^{20} = 0.6676

66.76% probability that the levee will NEVER fail in the next 20 years.

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