Explanation

The Poisson distribution is a discrete probability distribution that models the number of events (k) occurring in a fixed interval of time or space.

The probability mass function of the Poisson distribution is:

P(k) = (e^(-m) * (m^k)) / k!

where m is the mean (expected value) of the distribution, and e is the base of the natural logarithm (approximately 2.718).

If the mean (m) of a Poisson distribution is 1, then the probability of P(1) is:

P(1) = (e^(-1) * (1^1)) / 1! = 1/e ≈ 0.3679

So, the probability of P(1) is approximately 0.368, or 1/e.