118k views
3 votes
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.

User NewQueries
by
8.3k points

1 Answer

3 votes

Answer:

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.

User Yugene
by
7.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories