Question

(b) You are looking for needles in a field of haystacks. Suppose you search in n haystacks, and each time you perform a search of a haystack you find a needle with probability 0 independently of other searches. Show that the probability that you don't find a needle at all is [4] 0)" (1 - (c) You move to another field of haystacks. You are not sure whether there are needles in this field. If there are needles in the field then the situation is exactly as in part (b) If there are no needles in the field then the search of a haystack will definitely not be successful Let E be the event that there are needles in the field and let F be the event that you fail to find a needle. Derive the formula Р(F) 3D (1 — Ө)"Р(E) P(E"), stating carefully which theorems you use 8 (d) Let P(E) 687 haystacks and do not find a needle = 0.9 and e = 0.01. You search n = Conditional on this, find the probability that there are needles in the field, P(E|F) 7] [You may assume that 0.99687 = 0.001.] -

Answer 1

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