Question

A professor submitted a manuscript to a research journal for review. Historically, 19% of submitted manuscripts are accepted for publication in the journal. After the initial review, the manuscript can be sent to the journal editor, sent to the associate editors for additional review, or returned to the author for revisions. Of the manuscripts that were accepted for publication in the journal in the past, 47% were sent to the journal editor and 37% were sent to the associate editors for additional review. Of the manuscripts that were not accepted for publication in the journal in the past, 12% were sent to the journal editor and 32% were sent to the associate editors for additional review.

After the initial review, the professor's manuscript is returned to the author for revisions. Determine the probability that the professor's manuscript will be published in the journal.

Please explain in detail.

Answer 1

Here if

Event A is Submitted manuscripts are accepted for publication in the journal

Pr(Submitted manuscripts are accepted for publication in the journal) = 0.19

P(A) = 0.19

P(A^c) = 0.81

if B = Sent to journal editor

Pr(Sent to journal editor when selected for publication in the journal) = 0.47

P(B l A) = 0.47

if C = Sent to associate editor

Pr(Sent to associate editor when selected for publication in the journal) = 0.37

P(C l A) = 0.37

Pr(Sent to journal editor when not selected for publication in the journal) = 0.12

P(B l A^c) = 0.12

Pr(Sent to associate editor when not selected for publication in the journal) = 0.32

P(C l A^c) = 0.32

where P(A^c) = 1 - P(A) = 1 - 0.19 = 0.81

so if D = sent to author for revisions

P(D l A) = 1 - P(B l A) - P(C l A) =1 - 0.47 - 0.37 = 0.16

and

P(D l A^c) =1 - P(B l A^c) - P(C l A^c) =1 - 0.12- 0.32 = 0.56

Now as the question entailts, After the initial review, the professor's manuscript is returned to the author for revisions.

so as per total probability theorem

P(D) = P(D l A) * P(A) + P(D l A^c) * P(A^c) = 0.16 * 0.19 + 0.56 * 0.81 = 0.484

Now we have to find the probability that the professor's manuscript will be published in the journal

or mathematically,

Pr(A l D) = P(D l A) * P(A)/P(D) = (0.16 * 0.19)/0.484 = 0.0628 = 6.28%