Consider a point on the trans-australian highway, where two old wombats live. arrivals of cars at this point follow a poisson distribution; the average rate of arrivals is 1 car per 12 seconds. 1. one of these old wombats requires 12 seconds to cross the highway, and he starts out immediately after a car goes by. what is the probability he will survive?

(a) 0.114
(b) 0,736
(c) 0.368
(d) 0.184

(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

where

k = number of events in the given interval

= average number of events in the given interval.

In our specific case, the given interval of time is 12 seconds, and = 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)

So, the right answer is (C), 0.368