2.[10] Suppose that you have n accounts, each of which requires a password. Trudy has a dictionary and the probability that a password appears in Trudy's dictionary is p. a.[3] If you use the same password for all n accounts, what is the probability that your password appears in Trudy's dictionary? b.[3] If you use distinct passwords for each of your n accounts, what is the probability that at least one of your passwords appears in Trudy's dictionary? Show that if n= 1, your answer agrees with your answer to part a. c.[4] Which is more secure, choosing the same password for all accounts, or choosing different passwords for each account? Why