The kings treasurer ships 500 coins to a box and puts 1 coun

The king\'s treasurer ships 500 coins to a box and puts 1 counterfeit coin in each box. The king is suspicious, but, instead of testing all the coins in 1 box, he tests 1 coin chosen at random out of each of 500 boxes. What is the probability that he finds at least one fake? What is the probability of finding at least one fake it if the king tests 2 coins from each of 250 boxes?

Solution

probability of counterfeit coin in a bag= 1/500

-> m = 500 — (1/500) = 1, and so P (at least one fake) = .632

-> 2 coins from each of 250 boxes, then m =250 — = 1, and so the answer is again .632