Answer:
(C) 0.368
Step-by-step explanation:
The Poisson distribution models the probability that an event occurs k times in a given fix interval of time.
Is defined by the probability function
[tex]\huge P(k)=\frac{\lambda^ke^{-\lambda}}{k!}[/tex]
where
k = number of events in the given interval
[tex]\huge \lambda[/tex] = average number of events in the given interval.
In our specific case, the given interval of time is 12 seconds, and [tex]\huge \lambda[/tex] = 1 (1 car every 12 seconds).
As the old wombat requires 12 seconds to cross the highway, it might survive if only 1 car arrives over those 12 seconds.
The probability of this fact is P(1)
[tex]\huge P(1)=\frac{1^1e^{-1}}{1!}=e^{-1}=0.367879\approx 0.368[/tex]
So, the right answer is (C), 0.368
