Suppose $p$ is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and $p$ has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?

For a Poisson distribution with mean $\lambda = 3$, the probability mass function is:

The probability of observing fewer than 3 cars is:

Calculating each term:

• $P(p = 0) = \frac{e^{-3} 3^0}{0!} = e^{-3}$

• $P(p = 1) = \frac{e^{-3} 3^1}{1!} = 3e^{-3}$

• $P(p = 2) = \frac{e^{-3} 3^2}{2!} = \frac{9}{2}e^{-3}$

Summing these probabilities:

Hence, the correct option is C.