8. -4 points My Notes O Ask Your Teacher The Reviews editor for a certain scient

Question

8. -4 points My Notes O Ask Your Teacher 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 ong. Reviews are submitted in either Word or aTe·fors o treia s 70 o are n word whereas 50% of medium reviews are in word and 40% of long reviews are in word. Suppose a recent review is randomly selected (a) What isteobability that the selected review was submitted in Word format? (b) Ir the selected review was submitted in Word format, what are the posterior probabiies of it being short, medium, or long? (Round your answers to three decimal places.) short medium long Need Help? Talk to Tutor Read it

Explanation / Answer

p(Short) = .60
p(Medium) = .30
p(long) = .10

For short reviews, 70% in word, 50% of Long in Word, 40% of long in Word.

a. P(selected review was in Word ) = ?
= weighted probabity of writing short/med/long and writing the respective lengths in Word
= .60*.70 + .30*.50+.10*.40
=0.61

So, answer is .61

b.

P( short|written in word) = P(short and written in word | written in word) = .60*.70/.61 = .689
P(medium|written in word) = P(medium and written in word | written in word) = .30*.50/.61 = .246
P( long|written in word) = P(long and written in word | written in word) = .10*.40/.61 = .066

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