Hi, I have the following problem, but I am stuck on question D. I would really appreciate if someone could give me a hand! I know I have to use Bayes' theorem, but I don't know how :/. Thanks!
The problem says:
"A page of typescript contains 40 lines, with 80 characters per line. Each character has probability p=0.001 (independently of the others) of being erroneous.
A) What is the probability that a particular line contains no errors (i.e., no erroneous characters)?
B) What is the probability that a particular line contains more than one error?
C) What is the probability that the page contains exactly two errors?
D) Given that the page contains exactly two errors, what is the probability that they occur on separate lines?"
My solutions for A, B and C are (but I don't know how to work out D):
A)
p(x=0)=80C0*(0.001^0)*(0.999^80)=0.9231
B)
p(x=1)=80C1*(0.001^1)*(0.999^79)=0.0739
So,
p(x>1)=1-p(x=0)-p(x=1)=0.003
C)
p(x=2)=3200C2*(0.001^2)*(0.999^3198)=0.2087