Cryptography

4. (a) Determine the integer n such that the probability for two of n people having the same birthday is at least 9/10. (b) Suppose the 4-digit PINs are randomly distributed. How many people must be in a room such that the probability that two of them have the same PIN is at least 1/2 ? (Here " 4 digits" means that the PIN cannot start with a 0. .) Note: Pay special attention to the direction of the inequality in the formula(s) used for this