# Posterior Probability

#### maritimestudent

##### New member
Hello, Anybody have an idea how to do this?

Prior probabilities if diseases are based on the physician’s assessment of factors such as geographic location, seasonal influences, and occurrence of epidemics. Assume that a patient is believed to have one of two diseases, denoted D1 and d2. With P(D1)=0.60 and P(D2)=0.40, and that medical research shows a probability associated with each symptom that may accompany the diseases. Suppose that given diseases D1 and D2, the probabilities a patient will have symptoms S1, S2, or S3 are as follows

Disease Symptoms
S1 S2 S3
D1 0.15 0.10 0.15
D2 0.80 0.15 0.03

After finding that a certain symptom is present, the medical diagnosis may be aided by finding the revised probabilities the patient has each particular disease. Compute the posterior probabilities of each disease for the following medical findings;

A) Given the Patient has symptom S1, has D1
B)
Given the Patient has symptom S3, has D2
C)
Given the Patient has symptom S1, which disease does the patient more likely to have? D1 or D2? Show qualitatively.

Thank you!

#### Subhotosh Khan

##### Super Moderator
Staff member
Hello, Anybody have an idea how to do this?

Prior probabilities if diseases are based on the physician’s assessment of factors such as geographic location, seasonal influences, and occurrence of epidemics. Assume that a patient is believed to have one of two diseases, denoted D1 and d2. With P(D1)=0.60 and P(D2)=0.40, and that medical research shows a probability associated with each symptom that may accompany the diseases. Suppose that given diseases D1 and D2, the probabilities a patient will have symptoms S1, S2, or S3 are as follows

Disease Symptoms
S1 S2 S3
D1 0.15 0.10 0.15
D2 0.80 0.15 0.03

After finding that a certain symptom is present, the medical diagnosis may be aided by finding the revised probabilities the patient has each particular disease. Compute the posterior probabilities of each disease for the following medical findings;

A) Given the Patient has symptom S1, has D1
B)
Given the Patient has symptom S3, has D2
C)
Given the Patient has symptom S1, which disease does the patient more likely to have? D1 or D2? Show qualitatively.

Thank you!
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