My initial thought is to multiply L and p together to get a basic "success" rate, then divide by M, but there's no way this is that simple. I am not sure what the correct way is to solve this problem.
I have a Poisson-based question that I am not sure how to approach and solve. A processor receives groups of data bits with a Poisson arrival rate of L. The probability of an error in receiving an erroneous bit is p. The number of bits in a group of bits is Poisson with mean M. If there is no error correction (meaning retransmission) allowed, at what rate do groups of bits get to the processor?