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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?

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 titl class=

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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

[tex]P(M\cap S) = 30[/tex]

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

P(M/S)=3/5.


jayilych4real

The probability that the person's skin will clear up given that they used the medication is:

  • 3/5

What is Probability?

This refers to the likelihood of an event to occur based on certain conditions.

If we want to find the probability about whether the skin will clear up is:

We would assign S to represent the skin

M to represent medicine

Hence,

  • P(S) = 40
  • P(M)= 50

P(MnS) = 30

Using the conditional probability rule,

P9M/S)= P(MnS)/P(S) = 30/50

=3/5

Read more about probability here:
https://brainly.com/question/251701

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