The Reviews editor for a certain scientific journal decides whether the review f

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The Reviews editor for a certain scientific journal decides whether the review for any particular book should be short (1–2 pages), medium (3–4 pages), or long (5–6 pages). Data on recent reviews indicates that 50% of them are short, 30% are medium, and the other 20% are long. Reviews are submitted in either Word or LaTeX. For short reviews, 60% are in Word, whereas 40% of medium reviews are in Word and 20% of long reviews are in Word. Suppose a recent review is randomly selected.

short      medium      long      Assignment Three-Chex C } Owww.webassign.net/web/Student/Assignment-Responses/submit?dep:17195493 Apps G Google Google TranslateCSC 210 Final Project CSC 210 Final Prajecjay CSC 360 research with profess Applicant schools CSC 330 FINAL PROJE CSC110Other bookmarks Assignment Three-Chex C }Owww.webassign.net/web/Student/Assignment-Responses/last?dep:17195493 Apps G Google Google TranslateCSC 210 Final Project CSC 210 Final Prajecjay CSC 360 research with profess Applicant schools CSC 330 FINAL PROJE CSC110Other bookmarks 0/4 points | Previous Answers DevoreStat9 2 E 064 My Notes Ask Your Teach The Reviews editor for a certain scientific journal decides whether the review for any particular book should be short (1-2 pages), medim3-4 pages), or long (5-6 pages). Data on recent reviews indicates that 50% of them are short, 30% are medium, and the other 20% are long. Reviews are submitted in either word or LaTeX. For short reviews, 60% are in word whereas 40% of medium reviews are in word and 20% of long reviews are in word. Suppose a recent review is randomly selected (a) What is the probability that the selected review was submitted in Word format? 0.52 (b) If the selected review was submitted in Word format, what are the posterior probabilities of it being short, medium, or long? (Round your answers to three decimal places.) short medium 0.1923 long 0.5769 0.231 Need Help L Read Talk to a Tutor Submit AnswerSave Practice Another Version Submit Assignment Save Assignment Progress Home My Assignments Extension Request

Explanation / Answer

(A) Pr(short) = 0.5 ; Pr(Medium) = 0.3 and Pr(long) = 0.2

Pr (Word l SHort) = 0.60

Pr( WOrd l Medium) = 0.40

Pr(Word l Long) = 0.20

Probability that certain review is written in Word =

Pr (Word l SHort) * Pr(short) + Pr( WOrd l Medium) * Pr(Medium) + Pr(Word l Long) * Pr(long)

= 0.60 * 0.50 + 0.40 * 0.30 + 0.20 * 0.20 = 0.46

(b) Pr (Short l WOrd) = 0.60 * 0.50/ 0.46 = 0.652

Pr( Medium l Word) = 0.40 * 0.30/ 0.46 = 0.261

Pr(long l word) = 0.2 * 0.2/ 0.46 = 0.087

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