Question

An oil exploration company has determined at a site that the oil discovery probability is 0.65 per well. Assume that the oil exploration attempts, that is, the wells, are independent,
    (a) What is the probability that oil will be discovered on the first attempt?
    (b) What is the probability that oil will be discovered on the second attempt?
    (c) How many wells are needed in order to discover oil with a probability of 0.99?
    (e) Plot the number of attempts as a function of the probability in part (c) over the probability range from 0.85 to 0.9999.

Answer 1

a)

probability that oil will be discovered on the first attempt =0.65

b)

probability that oil will be discovered on the second attempt=P(failure on first attemt and succes on second)

=(1-0.65)*0.65=0.2275

c)

let number of wells needed are x;

hence P(at least one of the x wells have oil)=1-P(none have oil)=0.99

1-(1-0.65)^x =0.99

0.35^x =0.01

sovling above by taking log:

x=ln(0.01)/ln(0.35)=4.38 ~ 5

e)

from above given relationship: x=ln(1-p)/ln(0.35)

below is the graph: