Question

The incidence of eating disorders in the general population is .20. Many factors are taken into account like your score on the Eating Disorders Inventory. Previous work suggests that out of those people diagnosed with Eating Disorders, .70 of them score above 40 on the Eating Disorders Inventory (EDI) while .20 of those were not diagnosed with eating disorders scored above 40 on the EDI. What is the probability of being diagnosed with an Eating Disorder given that you scored above 40 on the EDI? Does giving the EDI improve the diagnostic accuracy for eating disor-ders? P(A/B)=P(ED/ Above40onEDI)= Does giving the EDI improve the diagnostic accuracy for eating disorders?

Answer 1

Let A denote the event that a random person from the population is diagnosed with Eating Disorders

And B be the event of scoring above 40 on the EDI

Thus, P(B|A) = 0.70 and P(B|A') = 0.20

Incidence of eating disorders in the general population = P(A) = 0.20

Thus, P(A') = 1 - P(A) = 0.80

Probability of being diagnosed with an Eating Disorder given that you scored above 40 on the EDI = P(A|B)

P(A|B) = = 7/15 = 0.4667

No, giving the EDI does not improve the diagnostic accuracy for eating disorders (Since P(A|B) is less than 0.5)