Cars and buses arrive at a bridge according to the independent Poisson processes at a rate of $3$ cars/minute and $1$ bus/ minute. What is the chance that strictly more buses arrive than cars in a given minute?
2026-04-03 07:43:03.1775202183
Approximation question
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You need to sum over $k$. The total probability is $\sum_{k=0}^\infty P(C=k)P(B \gt k)$. You have $C(k)=\frac {e^{-3}3^k}{k!}$ but I don't see a nice expression for $P(B \ge k)$. Maybe you are supposed to do it numerically.