Question 1195322: A Geiger counter counts the number of alpha particles from radioactive material. Over a long period of time, an average of 19 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.
Find the probability that at least two particles arrive in a particular 2 second period. Round your answer to four decimals.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! since the number is proportional to time, it would be 19/60 per second, and that is the specific Poisson parameter.
For a given second, it is e^(-19/60)*(19/60)^1/1!=0.2307
For two seconds, it would be parameter 38/60 or 19/30
this is e^(-19/30)*(19/30)^2/2!=0.1065, less likely because need two relatively uncommon events in a second rather than 1, but there is a little more time, just not enough to deal with the fact the number has doubled.
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