The Reviews editor for a certain scientific journal decides whether the review f

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 54% of them are short, 29% are medium, and the other 17% are long. Reviews are submitted in either World or LaTeX. For short reviews, it is half - to half, yet 35% 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? Only considering the formats, what is odds in favor of using the LaTeX format? When the selected review was submitted in LaTeX format, then what is the conditional probability of it being long? Hint Remember there are only three complementary categories for the reviews: short, medium and long, and there are only two complementary format for typing : Word and LaTeX

Explanation / Answer

SHORT REVIEWS = S = 54%................................ MEDIUM REVIEWS = M = 29 ............................. LONG REVIEWS = L = 17.............................. ..................................... SHORT REVIEW BREAK UP .... WORD ...W= 75%......................... LATEX..........L=25%.................................. ........................................................ MEDIUM REVIEW BREAK UP .... WORD ...W= 50%............................... LATEX..........L=50%............................... ......................................................... LONG REVIEW BREAK UP .... WORD ...W= 35%...................... LATEX..........L=65%........................ --------------------- A)...REVIEW IN WORD FORMAT .... IT COULD SHORT .....THEN....PS=0.54*0.75 = 0.405............... IT COULD BE MEDIUM .......PM=0.29*0.5 = 0.145 ....................... IT COULD BE LONG ...........PL= 0.17*0.35=0.0595................. SO TOTAL PROBABILITY = 0.6095...................ANSWER ------------------------------ B)....................LATEX FORMAT ...... IT COULD SHORT .....THEN....PS=0.54*0.25 = 0.135............... IT COULD BE MEDIUM .......PM=0.29*0.5 = 0.145 ....................... IT COULD BE LONG ...........PL= 0.17*0.65=0.1105................. SO TOTAL PROBABILITY = 0.3905................. SO ODDS IN FAVOUR OF LATEX ARE .....0.3905:1 =3905 : 10000 ------------------------------ C)................LATEX FORMAT ..PROBABILITY OF IT BEING LONG ... WE HAVE FROM B) .....IF THE FORMAT IS LATEX THEN IT COULD SHORT .....THEN....PS=0.54*0.25 = 0.135............... IT COULD BE MEDIUM .......PM=0.29*0.5 = 0.145 ....................... IT COULD BE LONG ...........PL= 0.17*0.65=0.1105................. SO TOTAL PROBABILITY = 0.3905................. HENCE PROBABILITY OF BEING LONG = 0.1105 / 0.3905 = 0.28297 .....ANSWER

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