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?

Answer 1

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

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

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

$$P(X=3)=C^{3-1}_{7-1}(1-p)^{7-3}p^3$$

$$=\dbinom{6}{2}(1-0.2)^4(0.2)^3=0.049152.$$