Kushchokhani wrote:
Abe, Beth and Carl each start to write a science fiction book. Their individual probabilities for completing their respective books are \(\frac{1}{2}\), \(\frac{1}{5}\) and \(\frac{1}{4}\). A completed science fiction book has a 20% chance of getting published. What is the probability that Beth or Carl, but not Abe, will get their book published?
A. \(\frac{11}{250}\)
B. \(\frac{9}{200}\)
C. \(\frac{99}{1250}\)
D. \(\frac{81}{1000}\)
E. \(\frac{1}{5}\)
Let us find the probability of each of them.
A: P to finish book \(\frac{1}{2}\), and 20% chance of this for publication => \(\frac{20}{100}*\frac{1}{2}=\frac{1}{10}\)
Thus P of not publishing the book = \(1-\frac{1}{10}=\frac{9}{10}\)
B: P to finish book \(\frac{1}{5}\), and 20% chance of this for publication => \(\frac{20}{100}*\frac{1}{5}=\frac{1}{25}\)
C: P to finish book \(\frac{1}{4}\), and 20% chance of this for publication => \(\frac{20}{100}*\frac{1}{4}=\frac{1}{20}\)
P of (B or C) = \(\frac{1}{20}+\frac{1}{25}-\frac{1}{20}*\frac{1}{25}=\frac{11}{125}\)
Thus P(B or C but not A) =\(\frac{11}{125}*\frac{9}{10}=\frac{99}{1250}\)
C
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