Answer to Question #238891 in Statistics and Probability for pearl

Question

Suppose that discarded cold drink cans are found along a particular road according to a Poisson process, with an average frequency of 3.2 cans every kilometre. What is the probability that a rubbish collector finds at least 2 cold drink cans in a given 200 metre stretch along this road?

Answer 1

QUESTION

Suppose that discarded cold drink cans are found along a particular road according to a Poisson process, with an average frequency of 3.2 cans every kilometer. What is the probability that a rubbish collector finds at least 2 cold drink cans in a given 200 meter stretch along this road?

SOLUTIN

The let $\lambda =3.2$

$P(X\ge)=\frac{(e^{-\lambda}*\lambda^k)}{(k!}$

Let us find the probability of getting at least 2 cold drinks in a given 200 meters

$P(x)=1-\frac{e^{-3.2}*3.2^0}{0!}-\frac{e^{-3.2}*3.2^1}{1!}$

$=1-0.04076-0.130439$

$=0.8288$

Answer: 0.8288 the probability of finding at least 2 cold dinks in a given 200 meters