A Geiger counter counts the number of alpha particles from radioactive material. Over a long period of time, an average of 14 particles per minute occurs. Assume the arrival of particles at the counter follows a Poisson distribution. Find the probability that at least one particle arrives in a particular one second period. Round your answer to four decimals.

0.2081 = 20.81% probability that at least one particle arrives in a particular one second period.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given interval.

Over a long period of time, an average of 14 particles per minute occurs. Assume the arrival of particles at the counter follows a Poisson distribution. Find the probability that at least one particle arrives in a particular one second period.

Each minute has 60 seconds, so

Either no particle arrives, or at least one does. The sum of the probabilities of these events is decimal 1. So

We want . So

In which

0.2081 = 20.81% probability that at least one particle arrives in a particular one second period.

answer: t=3

step-by-step explanation: