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. Reviews are submitted in either Word or LaTeX. For short reviews, 80% are in Word, whereas 50% of medium reviews are in Word and 30% 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?

Solution: Step1: It is given that a review editor decides the review for any particular book can be short ,medium or long. The recent reviews indicate that 60% of them are short, 30% are medium, and the other 10% are long. Reviews are submitted in either Word or LaTeX. For short reviews, 80% are in Word, whereas 50% of medium reviews are in Word and 30% of long reviews are in Word. Here a review is randomly selected. Step 2: a) We have to find the probability that the selected review in word. Here it is given that among 60% of short review 80% using word file and remaining using latex file.Also among 30% medium 80% using word 20% using latex. And among 10% of long 50% using word and 50% using latex Based on the given information we can make a probability table. Files Word Latex total short .48 .12 .6 Review Medium .15 .15 .3 .03 .07 .1 long So from the table we can find the probability that the selected review was submitted in a word. P(selected review was submitted in Word format)= 0.48+0.15+.03 = .66