Suppose a test for diagnosing a certain serious disease is successful in detecting the disease in 95% of all persons infected, but that it incorrectly diagnoses 4% of all healthy people as having the serious disease. suppose also that it incorrectly diagnoses 12% of all people having another minor disease as having the serious disease. if it is known that 2% of the population has the serious, 90% of the population is health and 8% has the minor disease, find the probability that a person selected at random has the serious disease if the test indicates that he or she does. use h to represent healthy, m to represent having minor disease and d to represent having serious disease. show the tree diagram and contingency table.

Step-by-step explanation:

Hello!

In the study population, there is an incidence of two diseases, a serious disease (D) and a minor disease (M).

There is a diagnostic test for the serious disease that successfully detects the disease (positive) in 95% of all persons infected (D). Symbolized P(+/D)=0.95

This test incorrectly diagnoses 4% (positive) of all healthy people (H) as having a serious disease. Symbolized P(+/H)= 0.04

And it incorrectly diagnoses 12% of all people having another minor disease as having a serious disease. Symbolized P(+/M)= 0.12

It is known in the population that:

2% of the population has a serious disease. P(D)= 0.02

90% of the population is healthy. P(H)= 0.90

8% of the population has a minor disease. P(M)= 0.08

I've attached a contingency table with the symbolized probabilities you need to calculate for each category.

Remember: Given the dependent events A and B a conditional probability of this events is defined as P(A/B)= P(A∩B)/P(B)

⇒ Then you can clear the probability of the intersection of both events as:

P(A∩B)= P(A/B)*P(B)

You can apply this to the asked probabilities:

P(+∩D)= P(+/D)*P(D)= 0.95*0.02= 0.019

P(+∩M)= P(+/M)*P(M)= 0.12*0.08= 0.0096

P(+∩H)= P(+/H)*P(H)= 0.04*0.90= 0.036

P(+) = P(+∩D) + P(+∩M) + P(+∩H)= 0.019 + 0.0096 + 0.036= 0.0646

P(-) = 1 - P(+) = 1 - 0.0646= 0.9354

P(-∩D)= P(D) - P(+∩D)= 0.02 - 0.019= 0.001

P(-∩M)= P(M) - P(+∩M)= 0.08 - 0.0096=0.0704

P(-∩H)= P(H) - P(+∩H)= 0.90 - 0.036= 0.864

Tree diagram and completed table attached below.

I hope it helps!

i want to die

what the hell man, i just want the points lol

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.