The reviews editor for a certain .scientific journal decides whether the review

Question

The reviews editor for a certain .scientific journal decides whether the review for any particular hook should be short (1-2 pages), medium (5-4 pages), or long (5-6 pages). Data on recent reviews indicates that 60% of them are short, 50% are medium, and the other 10% are long. Reviews are submitted in cither Word or a typesetting program called LaTeX. For short reviews, 80% are in Word, whereas 50% of medium reviews are in Word and 50% of long reviews are in Word. Suppose a recent review is randomly selected. What is the probability that the selected review was submitted in Word format? Suppose you are told the selected review was submitted in Word format. What is the probability that the review was medium in length?

Explanation / Answer

a)

Let

S, M, L = short, medium, long
W = word

Thus

P(W) = P(S) P(W|S) + P(M) P(W|M) + P(L) P(W|L)

P(W) = 0.60*0.80 + 0.30*0.50 + 0.10*0.30 = 0.66 [ANSWER]

******************

b)

P(M|W) = P(M) P(W|M) / P(W) = 0.30*0.50/0.66 = 0.227272727 [ANSWER]

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