Suppose the number of particles of contamination that occur

Suppose the number of particles of contamination that occur on an optical disk has a poisson distribution, and an average number of particles per centimeter squared of media surface is .1. The area of a disk under study is 100 squared centimeters.

a) Find the probability that 12 particles occur in the area of a disk under study.

b) Find the probability that zero particles occur in the area of the disk under study.

Solution

average number of particles on the disk = 0.1*100 = 10
u = 10

P(x) = (u^x) * (e^-u) / x!

a.
P(12) = (10^12) * (e^-10) / 12!
= 0.095

b.
P(0) = e^-10
= 4.54 * 10^-5