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There are 25 students at a bus stop. It is known that on average, 3 buses arrive at the bus stop in every 20 minutes. What is the probability that the waiting time for the next bus is at least 30 minutes? State the assumptions you need to compute the above probabilities.

Mathematics
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I believe it has got to do with Poisson distribution but I am not sure how to start from it. :(
So the number of buses has become the interval instead? But isn't time the only unit for the interval in poisson?
Also, the question asked for the assumptions that were made in computing the probabilities. What assumptions have we made in this calculation? I don't understand what kind of assumptions have we made.

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Other answers:

nice prof pic lol..
Also, to have X~Pois(20/3), and find P(X>=30)=1-P(X<30), The P(X<30) is very close to 1. This would make P(X>=30)=1-1=0, which looks weird.
wouldn't it be Poisson\(\displaystyle\left(\frac{3}{20}\cdot 30\right)\)=Poisson(4.5)
Calculate P(X=0)
Why calculate the probability of X=0?
0 buses arriving in the first 30 mins
OHH!!! wow!! This is smart!
time to teach..be back later
wow! this feels counter intuitive but somewhat logical. i wouldn't have thought of it. It's like so there is zero buses during the first 30mins and so this probability is as good as there is at least a bus after this first 30mins. thanks!!
ok sure! Thanks for you help!!!

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