Placebo
A group consisting of 300 people is participating in experimenting the placebo effect. A certain number of people got the real medicine, while the rest got the placebo. Of course, no one knew whether they got the real medicine or the placebo. After the examinations, 20% of the people who got the real medicine said that they felt no improvement, whilst 20% of people who got the placebo felt significant improvement. If 40% of all of the people that participated in the experiment said that they noticed improvement, how many people got the real medicine, and how many people got the placebo?
If the number of the people who got the placebo is , and the number of people who got the real medicine , input the answer as .
The answer is 3.
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1 solution
Because there are 300 people participating in the experiment, b = 300- a .
It is given that 20% of the people that were given the placebo felt improvement, or 0.2 a . 20% of the people with a medicine felt no improvent, so 80% did. This is equal to 0.8(300- a ) = 240 - 0.8 a . Therefore, in total (240-0.8 a ) + 0.2 a = 240 - 0.6 a felt improvement. This should be equal to 40% of the total group, or 0.4*300=120.
240 - 0.6 a = 120 -> 0.6 a = 120 --> a = 200 and therefore b = 100
The answer is 300/(200-100) = 3