Please explain this question in details , thanks! Suppose you go for a medical c

Question

Please explain this question in details , thanks!

Suppose you go for a medical checkup. Doctor administers a test to you for a serious disease. The test is 95% accurate (when tested on 100 patients with the disease, it identifies 95 of them as positive). It also is 99% accurate in identifying patients who do not have a disease (when tested on 100 disease free people, it only calls 1 out of 100 as positive) Assuming that you tested positive, which of the following are true? 0 O O a) b) c) d) If it is a rare disease (1 in 100 chance), there is close to 1% chance of actually having the disease If it is a moderately rare disease (10 in 100 chance), there is close to 10% chance of actually having the disease If it is a rare disease (1 in 100 chance), there is close to 50% chance of actually having the disease If it is a rare disease (1 in 100 chance), there is close to 10% chance of actually having the disease

Explanation / Answer

Ans:

Given that

P(positive/disease)=0.95

P(negative/not disease)=0.99

P(positive/no disease)=1-0.99=0.01

P( disease)=1/100=0.01

P(positive)=P(positive/disease)*P(disease)+P(positive/no disease)*P(no disease)

=0.95*0.01+0.01*0.99

=0.0194

Use Bayes Rule:

P(disease/positive)=P(positive/disease)*P(disease)/P(positive)

=0.95*0.01/0.0194=0.4897

i.e. close to 50%

Option C is correct

(if it is rare disease with 1/100 chance,there is close to 50% chance of actually having the disease)

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