Question

Of the wells drilled in a certain region, one-third are operated by Company A, half by Company B and one-sixth by Company C. The probability that a well owned by Company A produces oil is 0.4 . The corresponding probabilities for Company B and Company C are 0.3 and 0.5 , respectively. Given that a particular well produces oil, calculate the probability that it is owned by Company A.

Answer 1

To calculate the probability that a well producing oil is owned by Company A, we can use Bayes' theorem. Let A be the event that a well is owned by Company A, and let O be the event that a well produces oil.

Step-by-step explanation:

To calculate the probability that a well producing oil is owned by Company A, we can use Bayes' theorem. Let A be the event that a well is owned by Company A, and let O be the event that a well produces oil. We want to find P(A|O), the probability that a well is owned by Company A given that it produces oil.

According to the problem, one-third of the wells are operated by Company A, which means P(A) = 1/3. The probability that a well owned by Company A produces oil is given as 0.4, so P(O|A) = 0.4.

Using Bayes' theorem, we have:
P(A|O) = (P(O|A) * P(A)) / P(O)

To find P(O), the probability that any well produces oil, we can use the law of total probability:
P(O) = P(O|A) * P(A) + P(O|B) * P(B) + P(O|C) * P(C)

Given that P(O|B) = 0.3, P(O|C) = 0.5, P(B) = 1/2, and P(C) = 1/6, we can substitute these values to calculate P(O). Once we have P(O), we can substitute all the values into the formula above to calculate P(A|O).