I need your assistance with the following question:
The probability of a bus arriving at a given station over a 30-minute span of time at least once is 0.9. If you arrive with only 10 minutes to spare, what are the chances a bus arrives in this time span? (assuming the probability is constant throughout the time)
I assume I should use the Poisson distribution, so I did the following:
$$P(x\ge1)=1-P(x<1)=1-P(x=0)=0.9 $$
$$1-\frac{e^{-\lambda}\lambda^0}{0!}=0.9$$
$$\lambda=2.302585$$
But now what should I do with this $\lambda$? How can I proceed?
Thanks!
Best Answer
Hint: $\lambda$ is the expected number of buses in the 30 minute timeframe. So how do you calculate the probability that no busses appear in a 10 minute timeframe?