I've got a question as follows: A heavy container with chemical waste has been illegally dumped into the sea, and is now lying in a fixed but unknown position on the bottom of the sea. The container is believed to be situated in British territorial waters with probability 0.8. The Royal Navy are planning a search through the British territorial waters only, to try to find the container. If the container is situated in British territorial waters, then the probability that it will be found by such a search is 0.7 (while the probability that it will be overlooked is 0.3).
(i) Calculate the probability that the container will be discovered by this search through the British territorial waters
(ii) Suppose that this search through the British territorial waters turns out to be unsuccessful, i.e. the container is not found. Given this information, what is now the probability that the container is situated in British territorial waters?
For part (i) I think you use the conditional probability formula (P A given B) = P(A intersection B) / P (B). In this context, P(Found given British) = 0.7 and P(B) = 0.8 hence the answer is 0.8 x 0.7 = 0.56. Can someone confirm this?
For part (ii) I'm quite clueless about what to do
Thanks in advance