An oil company estimates that only 1 well in 24 will yield commercial quantities of oil. Assume that successful drilled wells represent independent events. If 5 wells are drilled, find the probability of obtaining a commercially successful well for the following number of times. (Round your answer to six decimal places.) exactly 1

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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 An oil company estimates that only 1 well in 24 will yield commercial quantities of oil. Assume that successful drilled wells represent independent events. If 5 wells are drilled, find the probability of obtaining a commercially successful well for the following number of times. (Round your answer to six decimal places.)

exactly 1
Expert Solution
Step 1

Given that,

The random variable X is well-yield commercial quantities of oil.

The successfully drilled wells represent independent events.

The sample size is n=4

Only 1 out of 24 will yield commercial quantities of oil

Therefore X will follow binomial.

X~B(n=5,p)

The pmf of the binomial distribution is as follows,

P(X=x)=Cxpx(1-p)n-x         ,x=0,1,2...n n

The combination is as follows,

Cx=n!(n-x)!×x!n

The factorial is as follows,

n!=n×(n-1)×...×1

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