dr.trovacek
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- Joined
- Apr 3, 2017
- Messages
- 23
Probability that some book is in a library is \(\displaystyle \frac{1}{3}\).
If the book is in the library, then it is equally probable that the book is on one of total 100 bookshelves. We checked 40 bookshelves and the book is not on any of them. What is the new probability that the book is in the library?
Solution: \(\displaystyle \frac{3}{13}\)
I think I have to use Bayes' Theorem, but I can't seem to calculate the probability of a specific book being in the library if 40 bookshelves are checked and this book is not on any of them.
So I'm starting like this:
\(\displaystyle H = \mbox{{the book is in the library}} \\
A= \mbox{{the book is not on any of the 40 checked bookshelves}}
\)
I think we are looking for: \(\displaystyle P(H|A) = P(\mbox{{book is in the library, if the book is not on any of the 40 checked bookshelves}})\)
So I need the values from the right side of the equation: \(\displaystyle P(H|A) = \frac{P(H) \cdot P(A|H)}{P(A)}\)
I have \(\displaystyle P(H)=\frac{1}{3}\), but is hard for me to make a distinction between \(\displaystyle P(A)\) and \(\displaystyle P(A|H)\), not in the terms of understanding the statement of the events, but rather the way to calculate them in this particular situation.
I tired to look at the event A as \(\displaystyle A= \mbox{{a book is on one of the 60 uncheked bookshelves}}\). I think it might be a problem that I kinda of started event A with a presumption that the book is already in the library.
Anyhow, I can't get the correct answer, this problem seems tricky to me.
Am I at least on the correct path?
Thanks in advance for any help
If the book is in the library, then it is equally probable that the book is on one of total 100 bookshelves. We checked 40 bookshelves and the book is not on any of them. What is the new probability that the book is in the library?
Solution: \(\displaystyle \frac{3}{13}\)
I think I have to use Bayes' Theorem, but I can't seem to calculate the probability of a specific book being in the library if 40 bookshelves are checked and this book is not on any of them.
So I'm starting like this:
\(\displaystyle H = \mbox{{the book is in the library}} \\
A= \mbox{{the book is not on any of the 40 checked bookshelves}}
\)
I think we are looking for: \(\displaystyle P(H|A) = P(\mbox{{book is in the library, if the book is not on any of the 40 checked bookshelves}})\)
So I need the values from the right side of the equation: \(\displaystyle P(H|A) = \frac{P(H) \cdot P(A|H)}{P(A)}\)
I have \(\displaystyle P(H)=\frac{1}{3}\), but is hard for me to make a distinction between \(\displaystyle P(A)\) and \(\displaystyle P(A|H)\), not in the terms of understanding the statement of the events, but rather the way to calculate them in this particular situation.
I tired to look at the event A as \(\displaystyle A= \mbox{{a book is on one of the 60 uncheked bookshelves}}\). I think it might be a problem that I kinda of started event A with a presumption that the book is already in the library.
Anyhow, I can't get the correct answer, this problem seems tricky to me.
Am I at least on the correct path?
Thanks in advance for any help
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