# Percent problem probability help?

In a certain city, 8% of adults have diabetes.
If a test correctly diagnoses a person with diabetes 95% of the time and incorrectly diagnoses a person without having the disease 2% of the time, determine the following:
a) What is the probability that a doctor that diagnoses a person as having diabetes...
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In a certain city, 8% of adults have diabetes.

If a test correctly diagnoses a person with diabetes 95% of the time and incorrectly diagnoses a person without having the disease 2% of the time, determine the following:

a) What is the probability that a doctor that diagnoses a person as having diabetes actually had diabetes?

b) What is the probability that a doctor that diagnoses a person as having diabetes doesn't have diabetes?

Please show your work.

If a test correctly diagnoses a person with diabetes 95% of the time and incorrectly diagnoses a person without having the disease 2% of the time, determine the following:

a) What is the probability that a doctor that diagnoses a person as having diabetes actually had diabetes?

b) What is the probability that a doctor that diagnoses a person as having diabetes doesn't have diabetes?

Please show your work.

Update:
To ignoramus: this is not a trick or made up question. I am NOT asking the probability if the doctor has diabetes.. geeze!

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