Question

An oil company conducts a geological study that indicates that an exploratory oil well should
have a 20 percent 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 the variance of the number of bad wells, if the oil company wants to
set up three producing wells?

Answer 1

a) This is a geometric distribution wit p=0.2.

$P(X=3)=(1-p)^2p=0.8^2*0.2=0.128.$

b) There is a negative binomial distribution with p=0.2, r=3.

$P(X=3)=C^{3-1}_{7-1}(1-p)^{7-3}p^3=C^2_6*0.8^20.2^3=0.049.$

c) Mean: $\mu=\frac{r}{p}=\frac{3}{0.2}=15.$

Variance: $\sigma^2=\frac{r(1-p)}{r^2}=\frac{3*0.8}{0.2^2}=60.$