Answer to Question #323844 in Statistics and Probability for Bless

Question

An oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil.

(a) What is the probability that the first strike comes on the third well drilled?

(b) What is the probability that the third strike comes on the seventh well drilled?

(c) What is the mean and variance of the number of wells that must be drilled if the oil company wants to set up three producing wells?

Answer 1

a) To find the requested probability, we need to find P(X=3). In this case, p=0.20,1−p=0.80,r=1,x=3

, and here's what the calculation looks like:

P(X=3)=(1−p)$^2 \cdot$ p=0.802⋅0.20=0.128

There is about a 13% chance that the first strike comes on the third well drilled.

b)We need to find P(X=7)

Use p=0.20,1−p=0.80,x=7,r=3

P(X=7)=(6 2)0.80$^4$⋅ 0.20$^3$=0.049

That is, there is about a 5% chance that the third strike comes on the seventh well drilled.

c)The mean number of wells is:

μ=E(X)=r/p=3/0.20=15

with a variance of:

σ$^2$ =Var(x)=r(1−p)/p$^2$ =3(0.80)0.20$^2$ =60