Question

Participants in a study of a new medication received either medication A or a placebo. Find P(placebo and improvement). You may find it helpful to make a tree diagram of the problem on a separate piece of paper.

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 the placebo, 62% reported no improvement.

I don't know how to do this at all, any hints or help would be nice. :)

Answer 1

The probability of p(placebo and improvement) is 7.6%.

Given that

Participants in a study of a new medication received either medication A or a placebo.

We have to find

The probability of P(placebo and improvement).

According to the question

Participants in a study of a new medication received either medication A or a placebo.

Let Probability that participants received medication A = P(M) = 0.80

Probability that participants received placebo = P(P) = 1 - P(M) = 1 - 0.80 = 0.20.

Because there are only two cases either medication A or a placebo.

Let I = event that there is an improvement.

Also, the Probability that participants reported improvement given that they had received medication A = P(I/M) = 0.76

The probability that participants reported no improvement given that they had received placebo = P(I'/P) = 0.62

So, Probability that participants reported improvement given that they had received placebo is,

=  P(I / P) = 1 - P(I' / P) = 1 - 0.62 = 0.38

Now, Probability of (placebo and improvement) = Probability that participants received placebo times Probability that participants reported improvement given that they had received placebo.

P(placebo and improvement) =  P(P)  times  P(I / P)  

P(placebo and improvement) =  0.20 times 0.38  =  0.076  or  7.6%

                         

Therefore, the required probability of p(placebo and improvement) is 7.6%.

To know more about Probability click the link given below.

https://brainly.com/question/743546