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. If you use the same password for...

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. If you use the same password for all n accounts, what is the probability that your password appears in Trudy's dictionary?

b. 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. Which is more secure, choosing the same password for all accounts, or choosing different passwords for each account? Why? See also Problem 21.