Welcome back to the DMV! The DMV has altered their system for assigning customers to service...

 

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Welcome back to the DMV! The DMV has altered their system for assigning customers to service counters. Now, when a customer enters the DMV, they press a button that randomly selects one of three letter generators. The selected letter generator then assigns one of six service counters to the customer, which are labelled A, B, C, D, E, and F. While two of these letter generators assign a service counter uniformly at random, the third generator is broken. The broken generator assigns the letter A with probability 1/2, then assigns the other five letters uniformly at random. (This is starting to cause service counter issues yet again...) (a) You arrive at the DMV and are assigned to service counter A. What is the probability that you selected the broken letter generator? (b) You use the same letter generator that you selected in part (a) to give you a new service counter assignment. What is the probability that it will assign you to service counter A... again? Welcome back to the DMV! The DMV has altered their system for assigning customers to service counters. Now, when a customer enters the DMV, they press a button that randomly selects one of three letter generators. The selected letter generator then assigns one of six service counters to the customer, which are labelled A, B, C, D, E, and F. While two of these letter generators assign a service counter uniformly at random, the third generator is broken. The broken generator assigns the letter A with probability 1/2, then assigns the other five letters uniformly at random. (This is starting to cause service counter issues yet again...) (a) You arrive at the DMV and are assigned to service counter A. What is the probability that you selected the broken letter generator? (b) You use the same letter generator that you selected in part (a) to give you a new service counter assignment. What is the probability that it will assign you to service counter A... again?