Bayes thoerem, can you check my solution please?

I'm terrible at statistics, i hope someone can help.

A ship sank into the sea and is now laying in a fixed but uknown position on the bottom of the sea in either British or foreign wanters. The probability that the ship is in British waters is 0.7. An extensive search is planned through the British sea to find the ship. If the ship is found in british waters, then the probability that it will be found by such a search is 0.8 (while the probability that it is overlooked is 0.2)
a) Give the probability that the ship will be found through british water?
Does bayes theorem apply in here?
A= ship is in british waters (0.7)
B = ship will be found (0.8)
P(A|B) = P(A^B)/P(B) = 0.56/0.8 = 0.7
b) if the ship is not found, what is the probability that ship is situated in british waters.
1 - 0.7 = 0.3

Is this correct?


Ambassador to the humans
10 minutes isn't quite long enough to start asking for people to help you out after the initial post.

Anywho - if you make the assumption that the probability the ship will be found is the same in non-british waters then your answer to the first one is ok. Your second one isn't correct. Just because a search doesn't find the ship in british waters doesn't mean that it isn't in british waters.


Ambassador to the humans
Note that this question is just basic probability and doesn't quite venture into the realm of statistics yet. It might be taught in a statistics course but that's mainly due to the necessity of understanding probability to be able to do anything interesting with statistics.