Answer: D. 60%
Step-by-step 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 :-
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)}\\\\=\dfrac{\dfrac{n(A\cap B)}{n(T)}}{\dfrac{n(B)}{n(T)}}\\\\=\dfrac{n(A\cap B)}{n(B)}\\\\=\dfrac{30}{50}=0.6[/tex]
In percent , P(A|B)=60%
Hence, the probability that the person's skin cleared up given that they used the medication = 60%
