An oil company conducts a geological research and concludes

An oil company conducts a geological research and concludes that an exploratory oil well has 0.15 chance of striking oil.

A) What is the probability that the third strike comes in the sixth well drilled?

B) Determine the expected value and variance of this distribution.

Let, p=probability of striking oil.

p=0.15

Here No. of success=No. of oil strikings=r=3

X:No. of failures before the 3rd success.

Then, X~NB(3,0.15)

(A)Now here No. of failures=6-3=3

Then,P[X=3]=0.0207267

(B)E(X)=pr/(1-p)=0.5294

V(X)=pr/(1-p)²=0.6228