. 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...

. 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 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 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?

(b) If the selected review was submitted in Word, what are the posterior probabilities of it being

short, medium, and long?