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## Homework Statement

On a country road an average of 30 cars pass per hour. Four hitch-hikers are standing near a sign and waiting for a lift. Supposing each driver is glad to take exactly one hitch-hiker, what is the probability that all the hitch-hikers will have found someone to take them to their destination after 10 minutes?

## Homework Equations

Poisson distribution

## The Attempt at a Solution

I'm not quite sure how to approach this. At first glance this seems to be a Poisson distribution since I'm searching for the probability of 4 cars passing by in 10 minutes, and any particular car passing by doesn't seem to (in my opinion) change the probability of any other car passing by.

So I took k=4, since I was interested in four cars passing by and I took lambda as 5, I got a probability of 0.17546 (17.5%), which intuitively seems a bit low considering lambda.

Is this naive approach correct or am I missing something?

Thanks for the help!

**Edit:**

A second after posting I realized that I've only calculated the probability for exactly four cars passing by, but the set conditions are also fulfilled if any number of cars greater than 4 pass by in those 10 minutes. How can I account for this?