The Reviews editor for a certain scientific journal decides whether the evie for

Question

The Reviews editor for a certain scientific journal decides whether the evie for any particular book should be short 1-2 pages medium 3-4 pages or long 5-6 pages). Data on recent evie s 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, 60% are in word, whereas 50% of medium reviews are in word and 30% of long reviews are in word. Suppose 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 long

Explanation / Answer

Solution :

Given that P(S) = 0.5 , P(M) = 0.2 , P(L) = 0.3 ; P(W/S) = 0.6 , P(W/M) = 0.5 , P(W/L) = 0.3

(a) The probability that the selected review was submitted in word format is 0.49

=> P(W) = P(W/S)*P(S) + P(W/M)*P(M) + P(W/L)*P(L)

= 0.6*0.5 + 0.5*0.2 + 0.3*0.3

= 0.49

(b) the selected review was submitted in word format, the posterior probabilities are

=> for Short

P(S/W) = P(W/S)*P(S)/P(W)

= 0.6*0.5/0.49

= 0.6122

=> For Medium

P(S/M) = P(W/M)*P(M)/P(W)

= 0.5*0.2/0.49

= 0.2041

=> For Long

P(S/L) = P(W/L)*P(L)/P(W)

= 0.3*0.3/0.49

= 0.1837

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