Question

# Suppose that at a particular bus stop, Brown buses arrive according to a Poisson process with...

Suppose that at a particular bus stop, Brown buses arrive according to a Poisson process with a constant rate of 3 per hour. The travel time on the Brown bus to your class is 7 minutes. (The Brown bus drops you off at your class.).  When you approach the bus stop, you see that you have just missed a Blue bus. Class starts in 20 minutes and it is exam day so you want to get to class as soon as possible. What is the probability that the Brown bus will get you to class on time? Answer to 3 decimal places.

Given,

To determine the probability that the Brown bus will get you to class on time

= 3/60 * 13

= 0.05*13

= 0.65

= 0.65

Now consider the poisson distribution

P(X = k) = e^-*^k / k!

P(X >= 1) = 1 - P(X = 0)

= 1 - e^-

= 1 - e^-0.65

= 1 - 0.522045776

= 0.477954223

= 0.478

Hence the probability that the Brown bus will get you to class on time is 0.478

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