Abe, Beth and Carl each start to write a science fiction book.

Question

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. \(\frac{1}{5}\)

A.  \frac{11}{250}

B.  \frac{9}{200}

C.  \frac{99}{1250}

D.  \frac{81}{1000}

E.  \frac{1}{5}

chetan2u · Answer

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

Crytiocanalyst · Answer

THe probability for B or C to complete the book but not both = 1/20 + 1/25 - 1/20*1/25 = 11/125

THe probability for A not to complete = 1-1/10 = 9/10

Therefore the required probability = 11 *9 /1250 = 99/1250

Therefore IMO C

Mugdho · Answer

What if the question asked, "What is the probability that Beth or Carl will get their book published?"

Would we still subtract the "Both" part ? I am confused about why the "Both" part is even needed?

chetan2u

Posted from my mobile device

chetan2u · Answer

Hi

You subtract BOTH when there is possibility of both happening together and is included in each case.

For example
When you choose P of Beth, it will contain when B publishes and C does not, and also when both B and C publish their books.
When you choose P of C, it will contain when C publishes and B does not, and also when both B and C publish their books.
So, both cases above contain 'both B and C', so it has to be subtracted once from total.

shaurya_gmat · Answer

Bunuel  or  chetan2u  ,can one of you help me verify what I might be missing in my approach -

B(publishes) * C (does not publish) * A (does not publish) + B (does not publish) * C (publishes) * A (does not publish)

So :
(1/5 * 1/5) * (3/4 (does not complete) + 1/4 * 4/5) * (1/2 + 1/2 * 4/5) (case 1)
 +
(4/5 + 1/5 * 4/5) * (1/4 * 1/5) * (1/2 + 1/2 * 4/5)

= 387/5000

What scenario am i overlooking / considering double to get a different answer than the OA ?

Bunuel · Answer

B(publishes) * C (publishes) * A (does not publish)

GMATPrecision · Answer

But the question says B OR a to publish, not both?

Kinshook · Answer

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?

The probability of Abe getting book published = 1/2*20% = 1/10
The probability of Abe not getting book published = 1 - 1/10 = 9/10

The probability of Beth getting book published = 1/5*20% = 1/25
The probability of Beth not getting book published = 1 - 1/25 = 24/25

The probability of Carl getting book published = 1/4*20% = 1/20
The probability of Carl not getting book published = 1 - 1/20 = 19/20

The probability that Beth or Carl getting book published = 1/25 + 1/20 - (1/25)(1/20) = 44/500 = 22/250

The probability that Beth or Carl, but not Abe, will get their book published = 22/250*9/10 = 99/1250

IMO C

Abe, Beth and Carl each start to write a science fiction book.

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards