Question

Participants in a study of a new medication received either medication A or a placebo. Find P(placebo and improvement). Of all those who participated in the study, 80% received medication A. Of those who received medication A, 76% reported an improvement. Of those who received a placebo, 62% reported no improvement... Please help, I have absolutely NO clue how to go about this. Maybe walk me through it? I don't just want the answer, please.

Answer 1

Answer:

7.6%

Step-by-step explanation:

What we know: 80% received medication A - well if 80% received the medication then that must mean that 20% did not recieve medication A, because we know 100% - 80% = 20%

Of those who received the placebo, 62% reported no improvement- well if 62% showed no improvement on the placebo that must mean that 38% DID show improvement on the placebo because we know that 100% - 62% = 38%

To find P (placebo and improvement) we multiply these two percentages- those who received a placebo, and those who showed improvement on the placebo. So 20% becomes 0.20 and 38% becomes 0.38. 0.20 x 0.38 = 0.076

Now we can convert this into a percentage! :) move the decimal over two places to the right and we get 7.6%

PSA CA AQUANDR Conditional Prob Quiz P2 Answer 100%

Answer 2

Hi, it will be really easy if you start out by plotting a tree diagram and tracing out the probabilities. Then you simply have to multiply the probabilities of placebo and improvement. 

-----80% Medication -----76% improvement
                                 -----24% no improvement
|
------20%Placebo --------62% no improvement
                           -----------38% improvement

Solving for P(placebo and improvement) = .20 x .38 = 0.076 = 7.6%