Question

2. A geological study indicates that an exploratory oil well drilled in a particular region should strike oil with probability 0.20. Find the probability that the third oil strike comes on the fifth well drilled.

Answer 1

3.07% probability that the third oil strike comes on the fifth well drilled.

Explanation:

For each oil drill, there are only two possible outcomes. Either there is a strike, or there is not. The probability that oil is striken in a trial is independent of other trials. 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.

Strike oil with probability 0.20.

This means that
`p = 0.2`

Find the probability that the third oil strike comes on the fifth well drilled.

2 strikes on the first four drills(P(X = 2) when n = 4) and strike on the fifth(0.2 probability).

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 2) = C_(4,2).(0.2)^(2).(0.8)^(2) = 0.1536`

0.2*0.1536 = 0.0307

3.07% probability that the third oil strike comes on the fifth well drilled.