Help: Poisson-based 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?

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.