Question

an oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil. assuming independence, what is that probability that the third strike comes on the seventh well drilled

Answer 1

Answer:

4.92% probability that the third strike comes on the seventh well drilled

Step-by-step explanation:

For each drill, there are only two possible outcomes. Either it is a strike, or it is not. Each drill is independent of other drills. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

20% chance of striking oil.

This means that $p = 0.2$

What is that probability that the third strike comes on the seventh well drilled

2 stikers during the first 6 drills(P(X = 2) when n = 6)[/tex]

Strike during the 7th drill, with 0.2 probability. So

$P = 0.2P(X = 2)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{6,2}.(0.2)^{2}.(0.8)^{4} = 0.2458$

Then

$P = 0.2P(X = 2) = 0.2*0.2458 = 0.0492$

4.92% probability that the third strike comes on the seventh well drilled