Probability assistance required
Down's syndrome is a disorder that affects 1 in 270 babies born to mothers aged 35 or over. A new blood test for the condition has a sensitivity (i.e. the probability of a positive test result given the Down's syndrome is present) of 89%, The specificity (i.e. the probability of a negative test result given that Down's syndrome is absent) of the new test is 75%.
a) What proportion of women over the age 35 would test positive on this new blood test?
b) A mother over age 35 receives a positive test result. What is the chance that Down's syndrome is actually present?
c) A mother over age 35 receives a negative test result. What is the chance that Down's syndrome is actually present.
For a) I managed to get the answer via a tree diagram, which is 25.237% However, I'm not sure how to attempt b) and c). How should I attempt this? Thanks