# 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:

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**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%.

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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