Question

A company is considering drilling oil wells. The probability of success for each well is 0.30. The cost of each well is $5 (in1000). Each well that is successful will be worth $60 (in 1000). 1) If the company drills 5 wells, the probability of at least one successful well is

1) If the company drills 5 wells, the probability of at least one successful well is

2) If the company drills 20 wells, the approximate probability of at most one successful well is

3) The expected profit and the standard deviation of profit in 5 drillings are

Answer 1

a)
If the company drills 5 wells, the probability of at least one successful well is
= 1- P(none of them is successful)
= 1- (1-p)^n

where p is probailityof success and n is number of wells drilled
p = 0.3 , n = 5
hence
1 - (1-0.3)^5
= 0.83193

b)
Probability of at most one successfull well
P(X = 0) + P(X = 1)
= 0.7^20 + 20 * 0.3 * 0.7^19
= 0.00763

c)

Y = net Profit = 60X - 5*5 = 60X -25

E(Y) = E(6

X -25)

= 60 E(Y) - 25

= 60* 5 * 0.3 - 25

= 65

sd (Y) = 60 * sd(X)

= 60* sqrt(npq) = 60*sqrt(5 *0.3* 0.7)

= 61.4817