Question

Can you answer this please fast

In a pandemic respiratory infectious disease caused by a virus A, the diagnostic test has been developed and carried out. Under this test when an individual actually has the disease with a positive result (true-positive test) occurs with the probability of 0.99, whereas an individual without the disease will show a positive test result (false-positive test) with the probability of 0.02. What is more, scientists have shown that 1 out of 1000 adults is confirmed positive and has this disease. a) Draw a tree diagram to describe the above event b) Find the probability that the individual has the disease if a randomly selected individual is tested and the result is positive.

Answer 1

a) The tree of the pandemic disease is as following -   

PEOPLE

0.001 0.999

0.99 0.01 0.02 0.98

b) probability = p(A/B) x p(A1) / [ p(A/B) x p(A1) + p(A/B) x p(B1) ]

  p(A/B) = 0.001( selected randomly)   p(A1) = 0.99 (true positive report) p(B1) = 0.02 (false positive report)

= 0.001 x 0.99 / ( 0.001 x 0.99 + 0.001 x 0.02 )

= 0.98