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juanma101285
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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 think I have to use Bayes' theorem, but I don't know how :/. Thanks!
"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?"
Bayes Theorem (I think)
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
D)
I do not know how to work out p(errors are on separate lines|page contains 2 errors). If Bayes' theorem is not needed, it would then be with the formula:
p(errors on separate lines|page has 2 errors)=p(errors on separate lines AND page has 2 errors)/p(page has 2 errors)... but how do I get the numerator for this division? :/
Homework Statement
"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?"
Homework Equations
Bayes Theorem (I think)
The Attempt at a Solution
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
D)
I do not know how to work out p(errors are on separate lines|page contains 2 errors). If Bayes' theorem is not needed, it would then be with the formula:
p(errors on separate lines|page has 2 errors)=p(errors on separate lines AND page has 2 errors)/p(page has 2 errors)... but how do I get the numerator for this division? :/