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

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

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) = (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