Question

A lab is trying to determine if a new medication is effective at reducing acne breakouts. The results are displayed in the Venn Diagram below in the attachment:

What is the probability that the person's skin cleared up given that they used the medication?

A. 10%
B. 20%
C. 30%
D. 60%

Answer 1

It's D.60 because 20x3 parts is 60

Answer 2

Answer: D. 60%

Explanation:

Let A = Event that person's skin cleared up

B= Event that person used the medication.

T be the total number of persons in this experiment.

From the Venn diagram , we have

n(A ∩ B) = 30

n (only A) = 10 and n(only B)=20

so , n(A)=n (only A) +n(A ∩ B) =10+30=40

n(B)=n(only B)+n(A ∩ B) =20+30=50

Now, the probability that the person's skin cleared up given that they used the medication :-

`P(A|B)=(P(A\cap B))/(P(B))\\\\=((n(A\cap B))/(n(T)))/((n(B))/(n(T)))\\\\=(n(A\cap B))/(n(B))\\\\=(30)/(50)=0.6`

In percent , P(A|B)=60%

Hence, the probability that the person's skin cleared up given that they used the medication = 60%