Question

The two-way frequency table below shows how many volunteers reported an improvementin their symptoms and whether they received a test medication or a placebo. What is theprobability that a volunteer reported an improvement in his or her symptoms, given that he orshe received the placebo? Round to the nearest tenth of a percent if necessary.MedicationPlaceImprovementNo improvement5318284339.4%74.6%19.7%50%None of the other answers are correct

Answer 1

Problem

Solution

For this problem we can define the following events:

A= Volunteer report improvement in his/her symptoms

B= the volunteer recieved the placebo

From the info given we can calculate the following probabilities:

P(A)= (53+28)/(142)= 0.570

P(B)= (28+43)/142= 0.5

Now we can calculate this probability:

P(A and B)= 28/142= 0.197

Finally we want to find this probability:

`P(A|B)=\frac{P(Aand\text{ B)}}{P(B)}`

And replacing we got:

P(A|B)= (0.197)/0.5=0.394

And that correspond to :

39.4%