In a drug study of a group of 500 patients, 150 patients responded positively to drug #1, 200 patients responded positively to drug #2 and 90 patients responded positively to both drug #1 and drug #2.

Question

8. In a drug study of a group of 500 patients, 150 patients responded positively to drug #1, 200 patients responded positively to drug #2 and 90 patients responded positively to both drug #1 and drug #2.

(a) What is the probability that a patient responds positively to either drug #1 or drug #2?

(b) What is the probability that a patient responds positively to drug #1 given that this patient responded positively to drug #2

Answer 1

So from the numbers

150-90 = 60 responded positively to drug 1 only

200 - 90 = 110 responded positively to drug 2 only

90 respond positively to both

500 - 60 - 110 - 90 = 240 respond positively to neither

(a) 500 patients. 60 + 110 + 90 = 260 respond positvely to 1 or 2, so 260 / 500 = 26 / 50 = 13/ 25

(b) 110 + 90 = 200 responded positively to drug 2. Of these 90 responded positively to drug 1.

So 90 / 200 = 9/20