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Archie sends one message to his girlfriend every morning. If he got replied, he would send another message(suppose adding the first sent one, there's a

Archie sends one message to his girlfriend every morning. If he got replied, he would send another message(suppose adding the first sent one, there's a maximum of 3 messages ); If he didn't get replied, he would send the same message again.

Suppose the probability of replied message from Archie's girlfriend is p, and it's independent of another message. Let K=[K1 K2 K3]' be a 3-dimensional random vector, Ki means the total messages Archie sent when he got replied to the "i" the times. Find PK(k).

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