A study of how people are using online services for medical consulting is descri

Question

A study of how people are using online services for medical consulting is described in a paper. Patients using a particular online site could request any combination of three services: specialist opinion, assessment of imaging studies (such as X-ray and MRI), and assessment of pathology results.

The accompanying table shows the combinations of services that were requested by 80 patients in their online consultations.

For a randomly selected patient from this study, define the events O, I, and A as given below.

O = event that the online consultation involves a specialist opinion

I = event that the online consultation involves the assessment of imaging studies

A = event that the online consultation involves the assessment of pathology results

Use the given information to find the following probabilities. (Round your answers to three decimal places.)

(a)

P(O)

(b)

P(not A)

(c)

P(O I)

(d)

P(I|O)

(e)

P(O|I)

Combination of Services Provided Number of
Patients Specialist opinion only 37 Assessment of pathology results only 1 Specialist opinion and assessment of
  pathology results only 12 Specialist opinion and assessment of imaging
  studies only 15 Specialist opinion, assessment of imaging
  studies, and assessment of pathology results 15

Explanation / Answer

Given that total number of patients (n) = 80

a) P(O) = O/n = 37/80 = 0.463

b) We have P(not A) = 1-P(A) = 1-A/n = 1-1/80 = 1-0.0125=0.988

c) P(O I) = 15/80 = 0.188

d) P(I|O) = P(I O) / P(O) = 0.188/0.463 = 0.406

e) P(O|I) =P(O I) / P(I)

Here and 'O' and 'I' are independent

P(O I) = P(O)P(I)

P(I) = P(O I)/P(O) = 0.188/0.463 = 0.406

P(O|I) =P(O I) / P(I) = 0.188/0.406 = 0.463

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