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

Question

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 60% of them are short, 30% are medium, and the other 10% are long. long reviews are in Word. Suppose a recent review is randomly selected (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 long

Explanation / Answer

Solution :

Given that P(S) = 0.6 , P(M) = 0.3 , P(L) = 0.10

P(W/S) = 0.6 , P(W/M) = 0.5 , P(W/L) = 0.4

(a) => The total probability that the selected review was submitted in word format is

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

= 0.6*0.6 + 0.5*0.3 + 0.4*0.10

= 0.55

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

for short :  

=> P(S/W) = P(S W)/P(W)

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

= 0.6*0.6/0.55

= 0.655

for medium :

=> P(M/W) = P(M W)/P(W)

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

= 0.5*0.3/0.55

= 0.273

for long :

=> P(L/W) = P(L W)/P(W)

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

= 0.4*0.10/0.55

= 0.073

Short : 0.655

Medium : 0.273

Long : 0.073

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