Probability problem - binomial distibution Please help me out, I need to solve this problem, unfortunately I don't have any good way to approach this task _The keeper of a certain king’s treasure receives the task of filling each of 100 urns with 100 gold coins. While fulfilling this task, he substitutes one lead coin for one gold coin in each urn. The king suspects deceit on the part of the sentry and has two methods at his disposal of auditing the contents of the urns. The first method consists of randomly choosing one coin from each of the 100 urns. The second method consists of randomly choosing four coins from each one of 25 of the 100 urns. Which method provides the largest probability of uncovering the deceit?_ The answers is "the second method" was solved by binomial distribution. The probabilities are 0.634 and 0.640 accordingly to the textbook "Understanding Probability" Thanks!

Hint: call $p_1$ the probability that a given urn reveals the deceit when one draws one coin from it and $p_4$ when one draws four coins. Your first step would be to compute $p_1$ and $p_4$. The text of the exercise probably means that the urn reveals the deceit if and only if the lead coin is the coin drawn, respectively is among the four coins drawn. Then $p_1$ and $p_4$ are very simple functions of $n$ the number of coins in each urn. Your second step would be to write the global probabilities $P_1$ and $P_4$ of uncovering the deceit as functions of $p_1$ and $p_4$ respectively. Sub-hint: consider the probabilities of _not_ uncovering the deceit.