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Find the probability?
A test for a certain disease is found to be 95% accurate meaning that it will correctly diagnose the disease in 95 out of 100 people who have the ailment. The test also 95% accurate for a negative result, meaning that it will correctly exclude the disease in 95 out of 100 people who do not have the ailment. For a certain segment of the population, the incidence of the disease is 4%.
If a person tests positive, find the probabilty that the person actually has the disease.
Help please!
1 Answer
- Anonymous1 decade agoFavorite Answer
Hey there, it's a bit of a tricky question, but i just did this in physics. it's a bayes theorem question, which tells us the probability of an event, given another event. ill apply it here:
You can read an explanation on wikipedia of bayes theorem.
The following means the probability of getting a positive result, given that you are positive:
p(+ve result | are +ve ) = 0.95 = 95%. we are given this
p(-ve result | are +ve ) = 0.05 = 5%. we are given this
p(-ve result | are -ve ) = 0.95 = 95%. we are given this
p(+ve result | are -ve ) = 0.05 = 5%. we are given this
p(+ve result) = p(+ve)*p(+ve result | are +ve) + p(-ve)*p(+ve result | are -ve ) = 0.04 * 0.95 + 0.96 * 0.05 = 0.086 = 8.6%
we want the prob. that you are positive given you tested positive.
p(are +ve | +ve result) = p(+ve result | are +ve ) * p(are +ve) / p(+ve result)
= 0.95 * 0.04 / 0.086
= 0.44 = 44%
surprisingly low....