Question

6. Bill hides a needle in one of n haystacks, labeled from 1 to n. The probability that he hides it in the ith haystack is p Now Zach is gonna look for the needle. If the neddle is in the haystack i and Zach decides to search this haystack, he will find the needle with probability q. Obviously, if Zach searches a haystack without the needle, then he will not find anything. At the end, Zach searched the ith haystack but did not find the needle. Show that the probability that the needle is, after all, in the haystack j is (1-qi)Pi i = i. Pj 1 liPi 2. diPi

Answer 1