SOLUTION: A study of two doctors finds that the probability of one doctor correctly diagnosing a medical condition is 93/1000 and the probability the second doctor will correctly diagnose a

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Question 1172413: A study of two doctors finds that the probability of one doctor correctly diagnosing a medical condition is 93/1000 and the probability the second doctor will correctly diagnose a medical condition is 97/100. What is the probability that at least one of the doctors will make a correct diagnosis? "9979/10,000" why is the answer.
Answer by math_helper(2461) About Me  (Show Source):
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This problem is easier to solve if you take the inverse:
P(at least one makes a correct diagnosis) = 1 - P(neither makes a correct diagnosis).

P(both doctors make incorrect diagnosis) = (7/100)*(3/100) = 21/10000
1 - 21/10000 =  (10000 - 21) / 10000  =  9979/10000