GMAThopeful wrote:
`Cralo' sea food restaurant is famous for fresh crab and lobsters. The restaurant has two tanks. The customers has to choose their dinner from the tanks. Tank A has 28 lobsters and 12 crabs. Tank B has 12 lobsters and 28 crabs. For Susan its a nasty experience to see her dinner alive, so she closes her eyes and randomly points at the lobsters or crabs. If she points at a lobster what is the probability that it is from tank A.
Answer Choices :
(A) 7/10
(B) 1/2
(C) 7/20
(D) 1/4
(E) 7/40
The answer is 7/10 (A).
Lets assume Pr(A|B) is the conditional probability of A given B, where
A - the lobster from tank A,
B - poining the lobster.
It means that Susan points the lobster first (event B), then the lobster is chosen from the tank A ( event A).
By using the Bayes' theorem we get
Pr(A|B) = Pr(B|A) * Pr(A) / Pr(B).
where
Pr(A) - picking the tank A regardless of any other information = 1/2 = 0.5 . Susan is treating both tanks equally, it is 0.5
Pr(B) - getting a lobster regardless of any information on the tanks. It is 40/80 = 1/2.
Pr(B|A) - getting a lobster in the tank A = 28/40 = 7/10.
Given all this information, we can compute the probabilty of Susan having selected tank A given that she got a lobster, as such:
Pr(A|B) = Pr(B|A) * Pr(A) / Pr(B) = 7/10 * 0.5 / 0.5 = 7/10. So the answer is (A).
hmm.. sounds strange that Pr(A|B) = Pr(B|A).... -)
P.S.
Actually, as for me, this is definitely the brainteaser.
I suggest to review the Bayes' theorem in wikipedia, especially example 1 "Conditional probabilities"
http://en.wikipedia.org/wiki/Bayes%27_theorem
and of course to check out the GMATClub's "Probability lesson"
http://www.gmatclub.com/content/courses ... bility.php
I was wondering such questions could be appeared at the Q49~51 score?