Question

A company is considering drilling oil wells. The probability of success for each well is 0.20. The cost of each well is $5 (in1000). Each well that is successful will be worth $60 (in 1000).

1) If the company drills 4 wells, the probability of at least one successful well is

2) If the company drills 40 wells, the approximate probability of at most one successful well is

3) The expected profit and the variance of profit in 4 drillings are

Answer 1

Let

p = probability of success for each well = 0.2

n = number of wells dug by the company

X = number of successful wells among n

Thus, X follows Binomial Distribution with n and p = 0.2

1) Company drills 4 wells

n = 4    wells

To find P(at least one successful well)

that is to find

Using Excel function BINOM.DIST we find the probability

P(at least one successful well) =

2)

n = 40    wells

To find P(at most one successful well)

that is to find

Using Excel function BINOM.DIST we find the probability

P(at most one successful well) =

3)

n = 4    wells

Then the Expected value of the Binomial Distribution of X(number of successful wells) is given by

E(X) = n*p = 4*0.2 = 0.8

Variance of X = V(X) = n*p*(1-p) = 4*0.2*0.8 = 0.64

C = cost of each well = $5000

W = worth of each well = $60000

Thus, Net profit for each well = W - C = 60000 - 5000 = 55000

Expected Profit = Expected Value of X * Net Profit

               = 0.8*55000

               = $44000        = $ 44 (in 1000)

Variance of Profit = Variance of X * Net profit

               = 0.64*55000

               = $35200         = $ 35.2 (in 1000)

Expected Profit =

Variance of Profit =