Probability of Poisson event occuring at least 3 times in given interval

Question

At a parking garage, automobiles enter at a rate of $1$ car every $2$ minutes. I need to find the probability that the number of automobiles entering the garage during any $2$ minute period exceeds $3$.

I know $\Pr(x \gt 3)= 1-\Pr(x\le 3)$.

So, $1-\left(e^{-1} + e^{-1} + \frac{1}{2} e^{-1} + \frac{1}{6} e^{-1}\right) \dots$.

There’s something (insufficiently) fishy about that distribution ... — Brian M. Scott, Dec 12 '13 at 04:36
As part of your answer, you may be expected to explain why you used the Poisson with parameter $1$ for the number of cars entering in the $2$-minute interval. — André Nicolas, Dec 12 '13 at 04:45
@BrianM.Scott I guess the "kills" was too subtle an indication that I understood? :) — John, Dec 12 '13 at 05:02

score -1 · Answer 1 · answered Jan 02 '17 at 02:25

About the statement

The Probability that the event exceeds 3 is not the same that the event happen at least 3 times.

The Probability that the event exceeds 3 is the same as the probability that the event happen at least 4 times.

Then we can perform

P(x>3) = 1 - P(x<=3)

Best Regards

Probability of Poisson event occuring at least 3 times in given interval

1 Answers1