Question

Bad gums may mean a bod mood. Researchers discovered that 85% of people who have suffered a bad mood had periodontal disease. Only 29% of healthy people have this disease. Suppose that in a certain community bad moods are rare, occuring with only 10% probability. If someone has periodontal disease, what is the probability that he or she will have bad mood?

Answer 1

24.6%

Explanation:

denote B: bad mood; H: healthy; D: periodontal disease

P(B|D)

=P(B,D) / P(D)

=P(B,D) / [P(D,B)+P(D,H)] ### law of total probability ###

=P(D|B)P(B) / [P(D|B)P(B) + P(D|H)P(H)]

=(0.85)*(0.1)/[(0.85)*(0.1) + (0.29)*(0.9)]

=0.245664739