A study of the impact of seeking a second opinion about a medical condition is described in a paper. Based on a review of a certain number of patient-initiated second opinions, the paper states, "Second opinions often resulted in changes in diagnosis (15.8%), treatment (39.4%), or changes in both (9.6%)."
Consider the following two events.
D = second opinion results in a change in diagnosis
T = second opinion results in a change in treatment
What are the values of P(D), P(T), P(D ∩ T)?
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From the information given in the paper, we can determine the values of P(D) and P(T), as well as calculate the value of P(D ∩ T).
P(D) = 15.8% = 0.158
P(T) = 39.4% = 0.394
To determine the value of P(D ∩ T), we add the percentage of cases that resulted in changes in both diagnosis and treatment:
P(D ∩ T) = 9.6% = 0.096
Therefore, the values are:
P(D) = 0.158
P(T) = 0.394
P(D ∩ T) = 0.096
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