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: A Venn Diagram titled Acne medicine probabilities is shown with two circles labeled used the medicine and skin cleared. Inside the used the medicine area is 20. Inside the skin cleared area is 10. In the intersection of the two circles is 30. The area outside the two circles is labeled 40. What is the probability that the person's skin cleared up given that they used the medication?

Answer 1

The probability that the person's skin cleared up given that they used the medication would be 60 percent. From the problem statement, the area given for each section represents the number of data that corresponds to used the medicine, skin cleared and for both. To determine the probability of the person's skin that cleared up using the medication, we simply divide the total number of persons that used the medicine, that is 30+20 = 50, to the number that represent for both which is 30. Therefore,

probability that the person's skin cleared up using the medication = 30 / 50 x 100 = 60 percent

Answer 2

Answer: 3/5 is the probability that person's skin cleared up given that they used the medication.

Step-by-step explanation:

let S represents skin cleared and M represents medicine used.

According to the given Venn diagram,

P(S) = 40

P(M)= 50

$P(M\cap S) = 30$

Thus by the definition of conditional probability,

If it is given that the skin is cleared then the probability that persons used the medicine,

P(M/S)=$\frac{P(M\cap S)}{P(S)}$=30/50= 3/5.

P(M/S)=3/5.