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 50% of them are short, 30% are medium, and the other 20% are long. Reviews are submitted in either Word or LaTeX. For short reviews, 70% are in Word, whereas 60% 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.) short medium long

Answer 1

Solutions - Page No -0 Given that, PCS) = 0.5, PCM) = 0.3, PLL) = 012 Pouls) = 0.7, P(W/M) = 0.6, PCW/L) = 0.3 (a) The total probability that the selected leviest was submitted in word format is, plud)= P(WIS) xp(s) + PC Wim) xpcm) +PCWL)xple) = 0.7 x 0.54 10:6 ) 2013 + 0.3 x 0.2 0-35+ 0.18 + 0.06 peval) = 0.59 Given that the selected review was submitted in word format, the posterior probabilities are for short : - P(Slo) - Pl Sow)/PCW) = PI W/S)x PCS) PCW) = 0.7 x 0.5 0.59 = 0.35 0.59 = 0.5932 = 0.593

Page No - @ For Medium in => PC M/w) = Pennw) (PCW). = P(w/m)xplm) PCW) = 0.6 X 0.3 0:59 0.18 0:59 -0.3050 20.305 For long :- P(L/W)= » P(Lnw)/PCW). = PIHIL)*P(L) PCHI) = 0.3* 02 0:59 = 0.6 0:59 = 10169 = 1.016 Shoot - 0.593 Medium = 0.305 Long = 1,016