My Notes Ask Your Teacher 10. ,-/4 points DevoreStat9 2.E.064. The Reviews edito

Question

My Notes Ask Your Teacher 10. ,-/4 points DevoreStat9 2.E.064. 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% o them are short 20% are medium, and he other 30% are long. Reviews are submitted in either Word or LaTeX or short reviews 60% are in ord whereas 50% of medium reve s are nwo 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 Need Help?ReadTaik to a Tutor

Explanation / Answer

Let

A ,B,C are the events that represents Short,Medium and long reviews respectively.

Let W is event that review typed in word so

Given

P(A)=0.5 P(B)=0.2 P(C)=0.3

Also

P(W|A)=0.6 P(W|B)=0.5 P(W|C)=0.3

a) we have to find P(W)

P(W)=P(A)P(W|A)+P(B)P(W|B)+P(C)P(W|C)

=0.5*0.6+0.2*0.5+0.3*0.3

=0.3+0.1+0.09=0.49

B)

We have to find P(A|W),P(B|W),P(C|W)

Short = P(A|W)=P(A and W)/P(W)=P(A)*P(W|A)/P(W)

=0.5*0.6/0.49=0.3/0.49=0.612

Medium: P(B|W)=P(B)P(W|B)/P(W)=0.2*0.5/0.49=0.1/0.49=0.204

Long:P(C|W)=P(C)P(W|C)/P(W)=0.3*0.3/0.49=0.09/0.49=0.183

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