$A$ doctor assumes that a patient has one of three diseases $d_1, d_2,$ or $d_3$. Before any test,he assumes an equal probability for each disease. He carries out a test that will be positive with probability $0.7$ if the patient has disease $d_1$,$0.5$ if the patient has disease $d_2$,and $0.8$ if the patient has disease $d_3$. Given that the outcome of the test was positive,what is the probability that the patient has disease $d_2$?
- A$\frac{1}{4}$
- B$\frac{1}{2}$
- C$\frac{1}{5}$
- D$\frac{1}{7}$
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