Statistic help problem!

[helloimage]

Problem is: When making cars, 15 out of every 25 need repair before sale. What is the probability that the next car out needs a repair?
Can someone show me how to start this? So far I got p=25, and k=15, but I am not sure about the other symbol...as I cannot find that in my calculator not the factorial symbol but the reversed v symbol. Can anyone help? Thanks.

 

[firemath]

By "the other symbol", do you mean the lambda?

 

[Romsek]

The number of cars that need repairs in a given interval of time has a Poisson distribution with rate \(\displaystyle \lambda = \dfrac{15}{25}=\dfrac 3 5\)

The Poisson distribution is memoryless. So I can set my time origin at any time during the manufacture
and the probability that the next car out needs a repair is just \(\displaystyle p(1)\)

\(\displaystyle p(k) = \dfrac{\lambda^k e^{-\lambda}}{k!}\)
\(\displaystyle p(1) = \dfrac{\lambda e^{-\lambda}}{1} = \dfrac 3 5 e^{-\frac 3 5} \approx 0.329287 \)

 

[helloimage]

Thank you so much guys! I have many more of these exercises and need a kick start lol.

 

[firemath]

I really didn't do much.