NMIMS MBA Assignment June 2023 (Decision Science)

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Bad gums may mean a bad mood. researchers discovered that 85% of people who have suffered a bad mood had periodontal disease, an inflammation of the gums. only 29% of healthy people have this disease. suppose that in a certain community bad moods are quite rare, occurring with only 10% probability. if someone has periodontal disease, what is the probability that he or she will have a bad mood?

Using Bayes' theorem:

P(BM|PD) = (P(PD|BM) * P(BM)) / P(PD)

To calculate P(PD), we need to use the law of total probability:

P(PD) = P(PD|BM) * P(BM) + P(PD|H) * P(H)


The probability that a person with periodontal disease will have a bad mood is approximately 25%.

Given:

  • 85% of people with bad mood have periodontal disease
  • 29% of people who are healthy have periodontal disease
  • In a certain community, only 10% population has a bad mood

To Find:

  • The probability of having a bad mood in the presence of periodontal disease in a community with 10% population having a bad mood

Solution:

  • Let the presence of periodontal disease= A
  • Let the presence of bad mood= B
  • according to Baye's Theorem: P()= P() * P(A)* 

  Wherein;

  • P() is the probability of having periodontal disease in presence of a bad mood= 0.85
  • P() is the probability of having a bad mood in presence of periodontal disease
  • P(A) is the probability of having the periodontal disease itself
  • P(B) is the probability of having a bad mood= 0.1

  To find P(A), we must use the formula as follows:

  • P(A) = P() * P(B) + P() * P(B')

  Where

  • P(not B) = 1 - P(B); which is the probability of not having a bad mood
  • P() is the probability of having periodontal disease without a bad mood

  Substituting the values we have:

  • P(A) = 0.85 * 0.10 + 0.29 * 0.90 = 0.344

  • Now we can find P(B|A):

  • P() = 

               = 0.247

Hence, the probability that someone with periodontal disease will have a bad mood is 0.247, or about 25%





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