Problem: IRS will audit 2 million taxpayers. Plus 1 million taxpayers will be audited by mail. Assume 100 million total taxpayers. Find the probability that in a random sample of 50 taxpayers there will be one audit and one mail-audit.
My approach:
For the audit: Used Poisson distribution with mu = 1 and x = 1.
P(1) = 1^1 * e^(-1) / 1! = 0.368.
For the mail-audit, I assumed the audit and mail-audit are independent, so I can use Poisson again with mu = 0.5 and x = 1. I get 0.303.
For both events, multiply, yielding 0.112.
What if I assume that the IRS will exclude auditees from mail-a

Question

Problem: IRS will audit 2 million taxpayers.  Plus 1 million taxpayers will be audited by mail.  Assume 100 million total taxpayers.  Find the probability that in a random sample of 50 taxpayers there will be one audit and one mail-audit.
My approach:
For the audit: Used Poisson distribution with mu = 1 and x = 1.
P(1) = 1^1 * e^(-1) / 1! = 0.368.
For the mail-audit, I assumed the audit and mail-audit are independent, so I can use Poisson again with mu = 0.5 and x = 1.  I get 0.303.
For both events, multiply, yielding 0.112.
What if I assume that the IRS will exclude auditees from mail-a