Five independent flips of a fair coin are made. find the probability that (a) the first three flips are the same; (b) either the first three flips are the same, or the last three flips are the same; (c) there are at least two heads among the first three flips, and at least two tails among the last three flips.

Anew test for ra is being developed. the test is administered to 750 patients with ra and 750 without ra. for the sake of the question, assume the prevalence of ra in this population is 50%. of the 750 patients with ra, 575 have a positive result. of the 750 patients without ra, 150 have a positive result. what is the positive predictive value of the new test? a575/(575+150) b. 600/(600+ 150) c. 575/(575+125) d. 600/(600+ 125)