[Math] Poisson Distribution practice problem

Question

I have just started to learn Poisson Distribution and I have no idea how to deal with the following practice from my textbook: Suppose the average amount of cars passing on a street per minute is Poisson (8.6). It takes a lady 5 seconds to cross a street and she waits for two cars to pass. What is the probability that she is safe to cross the street ?

Answer 1

The lady waits for 2 cars means:

the first 5 seconds, the lady waits because there is car passing. the second 5 seconds, the lady waits because there is car passing. the third 5 seconds, the lady waits because there is no car passing.

there is no car passing is P(0)=48.8% (you can do the math) there is car passing is 1-P(0)=41.2%

so the probability is 41.2% x 41.2% x 48.8%