4. 16 points DevoreSlal9 2 E 064 My Notes Ask Your Teach The Reviews editor for

Question

4. 16 points DevoreSlal9 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), medium (3-4 pages), or long (S-6 pages). Data on recent reviews indicates that 50% of them are short, 20% are medium, and the other 30% are long. Reviews are submitted in either word or LaTex. For short reviews, 80% are in word, whereas 60% of medium reviews are in word and 40% 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? (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 ong Need Help? ReadItTalk to a Tutor

Explanation / Answer

a)P(word format) =P(short and word+medium and word+long and word) =0.5*0.8+0.2*0.6+0.3*0.4=0.64

b)

P(short) =P(short and word)/P(word) =0.5*0.8/0.64=0.625

P(medium) =P(medium and word)/P(word) =0.2*0.6/0.64 =0.1875

P(long) =P(long and word)/P(word) =0.3*0.4/0.64 =0.1875

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