Probability Problem - Am I crazy?

Hello, I'm new in the Math Forum :)
I'm not a native English speaker, so I apologize for any mistakes in advance.

This problem was in my Mathematics test:

Quote:

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A ship has disappeared in the ocean. We admit that the situation has been caused by any of the following equiprobable causes:
sinking
sequestration
destruction by storm

To each case, the probability of the rescuing team manages to rescue all the crewmembers alive is, respectively, 4/5, 3/5 and 7/10

1st question - [ bla bla bla]
2nd question - We now know that 14 crewmembers were saved and that the cause of the disappearance was not the storm. After all, how many crewmembers were in the aforesaid ship?

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My teacher says the answer is 30.
I say the question makes absolutely no sense, as all we know are the odds (conditioned for each cause) for all of the crewmembers to survive. 14/30 would be the propotion between the number of rescues with all people saved and the total number of rescues.
I tried to explain my view to her, but she says she doesn't understand my problem with this question... Am I crazy or is she the one who seriously needs holidays?

It is tough to answer that question without knowing how many people were there in the ship to begin with.
More on Bayesian stats can be learned here Probability Puzzles: Understanding Bayesian Inference

Rethki,

The problem doesn't make sense to me as it is stated. Can you tell us what the 1st question was? I have a feeling there may be some additional information there that we are currently missing.