A social work researcher examined outcomes that provide insi

A social work researcher examined outcomes that provide insight into the relationship between psychotherapy and type of professional visited by the client ? a psychiatrist or a psychologist. The study results are summarized in the following table of probabilities: (a) What is the probability that a person will have success in psychotherapy? (b) Given that a person saw a psychiatrist, what is the probability that the person will have a good psychotherapy outcome? (c) What is the probability that a person saw a psychologist? (d) Given that a person has a poor psychotherapy outcome, what is the probability that s/he saw a psychologist?

Solution

a)

P(success) = P(psychologist good) + (psychiatrist good)

= 0.30 + 0.12

= 0.42

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b) P(good given that the person visited a psychiatrist)

P(good | psychiatrist) = P(good and psychiatrist) / P(psychiatrist)

= 0.12 / 0.55

= 12/55 --> ANSWER

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c)

P(psychologist) = 0.45 / 1.00 ---> 0.45

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d)

P(psycholo given that the outcome was poor)

P(psycholo | poor) = P(psycholo and poor) / P(poor)

= 0.15 / (0.15 + 0.43)

= 0.15 / 0.58

15/58 ---> ANSWER