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[10] 1. A certain company owns two machines that send numbers 1, 2, or 3 each time they they are activated. Machine A sends each of the three numbers with equal probability. Machine B sends 1's with with 50% probability and 2's and 3's with 25% probability each. A machine is chosen at random and activated seven times sending 1,3,3,2,1,2,1. What is the probability that the machine chosen was machine B? [10] 2. A nine character long password is to be created using lower-case letters, four special characters {L @, #, $} and digits. For the password to be valid, it must contain at least one lower-case letter, one of the given special characters and one digit. What is the probability that a randomly generated nine character password is valid? Assume that the password is generated using only the lowercase letters, the given special characters and digits