Suppose a machine tracks the number of vehicles that cross a particular bridge on a given day, but the machine is not gu

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Suppose a machine tracks the number of vehicles that cross a
particular bridge on a given day, but the machine is not guaranteed
to work perfectly. The machine independently detects each arriving
vehicle with probability p. Suppose also that the number of
vehicles arriving in a given day N is a Poisson random variable
with parameter λ. Let Z be the number of vehicles counted.
What is the probability that Z differs from N by at most two?(I
need all step, and final answer)