Two doctors

Doctor A will determine the correct diagnosis with a probability of 89% and doctor B with a probability of 75%. Calculate the probability of proper diagnosis if both doctors diagnose the patient.

Correct answer:

p =  97.25 %

Step-by-step explanation:

q1​=89%=10089​=0.89 q2​=75%=10075​=43​=0.75  p(A∪B) = p(A)+p(B) − p(A∩B)  q=q1​+q2​−q1​⋅ q2​=0.89+0.75−0.89⋅ 0.75=400389​=0.9725  p=100⋅ q=100⋅ 0.9725=97.25%

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Showing 1 comment:
Math student
To calculate the probability of proper diagnosis if both doctors diagnose the patient, we can use the multiplication rule of probability:

P(A and B) = P(A) * P(B)

where P(A and B) is the probability that both doctors A and B diagnose the patient correctly, P(A) is the probability that doctor A diagnoses the patient correctly, and P(B) is the probability that doctor B diagnoses the patient correctly.

We are given that the probability of correct diagnosis by doctor A is 0.93 (or 93%) and the probability of correct diagnosis by doctor B is 0.79 (or 79%). Therefore:

P(A) = 0.93
P(B) = 0.79

To find the probability that both doctors diagnose the patient correctly, we multiply the probabilities:

P(A and B) = P(A) * P(B) = 0.93 * 0.79 = 0.7347

Therefore, the probability of proper diagnosis if both doctors diagnose the patient is approximately 0.7347 or 73.47%.





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