# Number of accidents follows the Poisson distribution w/ rate of 0.5 car accidents/day

#### Georgegr

##### New member
I need help with this probability problem.
The number of car accidents that happen in a specific region follows the Poisson distribution with a rate of 0.5 car accidents per day
Calculate (approximately) the probability to wait more than 60 days for the occurrence of the 40th car accident.

Consider X=number of car accidents. Then X follows Poisson distribution with λ=0.5 and P(X=1)=0.3032
I consider the random variable
Y=number of days till the 40th car accident
Then
[FONT=MathJax_Math-italic]Y [/FONT][FONT=MathJax_Math-italic]follows [FONT=MathJax_Main]Negative Binomial(k=40,p=0.3032) [/FONT][FONT=MathJax_Main]and the asked probability is [FONT=MathJax_Math-italic]P(Y>60)[/FONT][FONT=MathJax_Math-italic].
Is my solution right?
[/FONT][/FONT][/FONT]

#### tkhunny

##### Moderator
Staff member
I need help with this probability problem.
The number of car accidents that happen in a specific region follows the Poisson distribution with a rate of 0.5 car accidents per day
Calculate (approximately) the probability to wait more than 60 days for the occurrence of the 40th car accident.

Consider X=number of car accidents. Then X follows Poisson distribution with λ=0.5 and P(X=1)=0.3032
I consider the random variable
Y=number of days till the 40th car accident
Then
[FONT=MathJax_Math-italic]Y [/FONT][FONT=MathJax_Math-italic]follows [FONT=MathJax_Main]Negative Binomial(k=40,p=0.3032) [/FONT][FONT=MathJax_Main]and the asked probability is [FONT=MathJax_Math-italic]P(Y>60)[/FONT][FONT=MathJax_Math-italic].
Is my solution right?
[/FONT][/FONT][/FONT]
I'm not quite following your work. It may be okay, I suppose, but once you said "Negative Binomial", I lost interest.

In my opinion, there real beauty of Poisson is its scalability. If you have 0.5 car / day, you also have 40 cars / 80 days and 30 cars / 60 days. Can we get this anywhere near your solution?