An oil inspector will drill a succession of holes in a givenarea to find a produ

Question

An oil inspector will drill a succession of holes in a givenarea to find a productive well. The probability that he issuccessful on a given trial is 0.2 a. What is the probabilty that the fifth hole drilled is thefirst to yield a productive well? b. If the prospector can only afford to drill at most 10holes, what is the probability that he fails to find a productivewell? An oil inspector will drill a succession of holes in a givenarea to find a productive well. The probability that he issuccessful on a given trial is 0.2 a. What is the probabilty that the fifth hole drilled is thefirst to yield a productive well? b. If the prospector can only afford to drill at most 10holes, what is the probability that he fails to find a productivewell?

Explanation / Answer

p=.2;   1-p=.8 a)P(first success on 5thhole)=(1-p)4p=(.8)4(.2)=.082 b)Let X=number of producing wells drilled. X isBinomial(n=10,p=.2) P(X=0)=C(10,0)(.2)0(.8)10=.107

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