Suppose one of the lab assistants accidentally mixed two patients' blood samples before they were distributed to the vials. Which of the following correctly represents the set of all possible numbers of positive test results out of the eight vials?
Explanation:
Assuming patient 1 has the disease.
Case 1: Those patient’s blood is mixed which have no common vial. ∴ Patient 1 and 16’s samples are mixed. In this case all 8 vials i.e., A to D will have the blood of diseased patient. ⇒ All 8 vials will test positive.
Case 2: Those patient’s blood is mixed which have exactly 1 common vial. ∴ Patient 1 and 15’s samples are mixed. In this case 7 vials i.e., A to F and H will have the blood of diseased patient. ⇒ 7 vials will test positive.
Case 3: Those patient’s blood is mixed which have exactly 2 common vials. ∴ Patient 1 and 13’s samples are mixed. In this case 6 vials i.e., A to D, F and H will have the blood of diseased patient. ⇒ 6 vials will test positive.
Case 4: Those patient’s blood is mixed which have exactly 3 common vials. ∴ Patient 1 and 9’s samples are mixed. In this case 5 vials i.e., A, B, D, F and H will have the blood of diseased patient. ⇒ 5 vials will test positive.
Case 5: Those patient’s blood is mixed which don’t have the disease. ∴ Patient 2 and 3’s samples are mixed. In this case 4 vials i.e., B, D, F and H will have the blood of diseased patient. ⇒ 4 vials will test positive.
∴ Either 4, 5, 6, 7 or 8 vials can test positive.
Hence, option (b).
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