Probability: 2018 #38

Problem 38. When investigating a lease your geologist estimates there is a 40% chance of finding marketable oil, an 80% chance of finding marketable gas, and a 30% chance of finding marketable oil with marketable gas. The estimated probabilities of finding any marketable hydrocarbon, only marketable gas, and no marketable hydrocarbons at all (respectively) are:

(A) 90%, 50%, 10%
(B) 85%, 60%, 15%
(C) 90%, 60%, 10%
(D) 80%, 40%, 20%

For many, even most, this problem is difficult to do in six minutes. Why? It's uncommon, not intuitive, and working out the logic takes too much time to learn on the spot. However, the problem style is in the Guidebook as well as Mian's (I think), and since I also remember this sort of thing in the SPE HS (I think) it's definitely fair game. Note I cranked this one out fast, so please let me know if you find a typo!

Solution: A=oil, B=gas
P(A or B) = P(A) + P(B) – P(A and B) = 0.4 + 0.8 – 0.3 = 0.9
P(B only) = P(B) – P(A and B) = 0.8 – 0.3 = 0.5
P(neither A or B) = 1 – P(A or B) = 1 – 0.9 = 0.1
Key 0.4+0.8-0.3=0.9; 0.8-0.3=0.5; 1-0.9=0.1 (A)