# Two doctors

Doctor A will determine the correct diagnosis with a probability 93% and doctor B with a probability 79%. Calculate probability of correct diagnosis if patient is diagnosed by both doctors.

Result

p =  98.53 %

#### Solution:

$q_{ 1 } = 93 \% = \dfrac{ 93 }{ 100 } = 0.93 \ \\ q_{ 2 } = 79 \% = \dfrac{ 79 }{ 100 } = 0.79 \ \\ \ \\ q = q_{ 1 } + q_{ 2 } - q_{ 1 } \cdot \ q_{ 2 } = 0.93 + 0.79 - 0.93 \cdot \ 0.79 = 0.9853 \ \\ \ \\ p = 100 \cdot \ q = 100 \cdot \ 0.9853 = \dfrac{ 9853 }{ 100 } = 98.53 = 98.53 \%$

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