Question

A drilling company has estimated a 40% chance of striking oil successfully for their new well. A detailed test is usually scheduled for more information.Experience shows that 90% wells are scheduled for the test. Thirty four percent wells are successful and have detailed test.

(i) Obtain the probability of an unsuccessful attempt with no test done.

(ii) Also find the probability that an attempt was unsuccessful while it was known that no test was performed.

Answer 1

P(successful attempt) = 0.4

P(scheduled for test) = 0.9

P(successful and have detailed test) = 0.34

I) P(unsuccessful attempt and no test done) = 1 - (P(successful attempt or have detailed test)

= 1 - (P(successful attempt) + P(scheduled for test) - P(successful attempt and have detailed test))

= 1 - (0.4 + 0.9 - 0.34)

= 0.04

Ii) P(unsuccessful | no test was performed) = P(unsuccessful and no test has performed) / P(no test was performed)

= 0.04 / (1 - 0.9)

= 0.4