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 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 40% 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? (Round your answers to three decimal places.)

Answer 1

W : Event of review was submitted in word format

: Event of review was submitted in Latex(Not Word) format

S : Event of review is short

M : Event of review is medium

L : Event of review is long

Given,

60% of the review are short, 30% are medium, and the other 10% are long i.e

P(S) = 0.60 ; P(M) = 0.30 ; P(L) = 0.10

short reviews, 80% are in Word, whereas 40% of medium reviews are in Word and 30% of long reviews are in Word

P(W|S) = 0.80 ; P(W|M) = 0.40 P(W|L) =0.30

a)

Probability that the selected review was submitted in Word format = P(W)

P(W) = 0.63

Probability that the selected review was submitted in Word format = 0.63

b)

If the selected review was submitted in Word format,

the posterior probabilities of review being short : P(S|W)

From a)

If the selected review was submitted in Word format,  the posterior probabilities of review being short = 0.7619

If the selected review was submitted in Word format,

the posterior probabilities of review being medium: P(M|W)

From a)

If the selected review was submitted in Word format,  the posterior probabilities of review being medium = 0.1905

If the selected review was submitted in Word format,

the posterior probabilities of review being long: P(L|W)

From a)

If the selected review was submitted in Word format,  the posterior probabilities of review being long= 0.0476

If the selected review was submitted in Word format,  the posterior probabilities of review being short = 0.7619

If the selected review was submitted in Word format,  the posterior probabilities of review being medium = 0.1905

If the selected review was submitted in Word format,  the posterior probabilities of review being long= 0.0476