Question

An oil company conducts a study that indicates that an exploratory oil well should have a 25% chance of striking oil. Assume independence between different wells.

(a) if the company drilled 8 exploratory wells, what is the probability that the strike success in at least 2 wells.

(b) what is the average number of oil wells that they have to drill until the first strike comes?

(c) What is the probability that it will take more than 5 attempts to get the first strike of oil

(d) what is the probability that the fourth strike comes on the 10th well drilled?

Answer 1

part a)

X ~ B ( n = 8 , P = 0.25 )

P ( X >= 2 ) = 1 - P ( X <= 1 ) = 1 - 0.3671 = 0.6329

Part b)

X Geometric (P = 0.25 , q = ( 1 - P ) = 0.75 )

Mean = 1 / P = 1 / 0.25 = 4

Part c)

X Geometric (P = 0.25 , q = ( 1 - P ) = 0.75 )

P ( X > 5 ) = 1 - P ( X <= 5 ) = 1 - 0.7627 = 0.2373

Part d)

X ̴ NB (P = 0.25 , q = ( 1 - P ) = 0.75 k = 4 )

P ( X = 10 ) = 0.0584