1. **Problem statement:** On average, 3 traffic accidents per month occur at a certain intersection. We want to find the probability that fewer than 6 accidents occur in any given month. 2. **Formula used:** This is a Poisson distribution problem where the average rate $\lambda = 3$ accidents per month. The probability of exactly $k$ events is given by: $$P(X=k) = \frac{\lambda^k e^{-\lambda}}{k!}$$ 3. **What is asked:** We want $P(X < 6)$, which means $P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)$. 4. **Using the Poisson probability sums table:** The table provides cumulative probabilities $P(X \leq k)$ for Poisson distributions. 5. **Calculate:** $$P(X < 6) = P(X \leq 5)$$ From the Poisson table for $\lambda=3$, $$P(X \leq 5) = 0.9161$$ 6. **Answer:** The probability that fewer than 6 accidents occur in any given month is $$\boxed{0.9161}$$