Question

In a scientific journal, 60% of articles are short, 30% are medium, and 10% are long length. Articles are submitted in either Word or LaTeX. 80% of short articles are submitted on Word, 50% or medium are on Word, and 30% of long are on Word. A random article is selected. If the article was submitted on word, what are the posterior probabilities of it being short, medium, and long?

Answer 1

Given,

P(Short) = 0.60

P(Medium) = 0.30

P(Long) = 0.10

P(Word | Short) = 0.80

P(Word | Medium) = 0.50

P(Word | Long) = 0.30

Hence by Bayes' theorem:

Posterior probability of short

= P(Short | Word)

= 0.7273

Posterior probability of medium

= P(Medium | Word)

= 0.2273

Posterior probability of long

= P(Long | Word)

= 0.0455