Question

URGENT!

SHOW NOT ONLY ANSWER BUT ALSO STEPS.

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 50% of medium reviews are in Word, and 30% of long reviews are in Word. Suppose a recent review is randomly selected. 1) What is the probability that the selected review was submitted in Word format? 2) 2) If the selected review was submitted in Word format, what are the posterior probabilities of it being short, medium, or long?

Answer 1

SOLUTION:

Let A₁,A₂, and A₃ denote the events that a review is short, medium, and long , respectively. Let B denote the event that a review is in word. Then 'B' is the event a review is in Latex. we are given the following probabilities.

(a) Use the law of total probability to find P(B) as shown below :

= 0.66

Therefore , the probability that the selected review was submitted in words format is 0.66

(b) Use the Bayes theorem to find posterior probabilities as shown below:

Therefore, the posterior probability that it s short if selected review was in word format is 0.7273.

Therefore, the posterior probability that it is medium if selected review was in word format is 0.2273.

Therefore, the posterior probability that it is long if selected review was in word format is 0.0455.