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 60percentage of them are short, 30percentage are medium, and the other 10percentage are long. Reviews are submitted in either Word or LaTex. For short reviews, 80percentage are in Word, whereas 50percentage of medium reviews are in Word and 40percentage 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.)

Explanation / Answer

we hav to find the probability for word formate

word formate can by all three types (short to long)

probability from short formate is = probability of short type *probability of word formate =0.6*0.8 =0.48

asme as for medium type probability= 0.3*0.5 =0.15

from long type probability = 0.1*0.4 =0.04

total probability = 0.48+0.15+0.04 =0.67

b)

now its conferm that selected review is in word formate

we habe calculated that P(W) =0.67

probability of that word formate is from short type is = probability of gating select word from word (P(WS)) / P(W) = 0.48/0.67=0.7164

SAME AS FOR MEDIUM TYPE probability = P(WM)/P(W) =0.15/0.67 = 0.2239

probability from long type =P(WL)/P(W) = 0.04/0.67=0.0587

thanks

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