Answer: D. 43 %
Step-by-step explanation:
Let M is the event of receiving medicine,
M' is the event of not receiving medicine,
C is the event of clear skin.
Then According to the question,
Total size of the sample space, n(S) = 100
Number of patient who get the medicine, n(M) = 40
Number of patient who do not get the medicine, n(M') = 60
Number of patient who received the medication reported clearer skin at the end of the study, [tex]n(M\capC) = 15[/tex]
Therefore, the probability that patient who received the medication reported clearer skin at the end of the study, [tex]P(M\cap C) = \frac{n(M\cap C)}{n(S)} = \frac{15}{100} = 0.15[/tex]
Number of patient who who did not receive the medication reported clearer skin at the end of the study, n(M\capC) = 20.
Thus, the Number of patient who cleared the skin, n(C) = 15 + 20 = 35
And, the probability that the patient cleared their skin, [tex]P(C) = \frac{n(C)}{n(S)} = \frac{35}{100} = 0.35[/tex]
Therefore, the probability that a patient chosen at random from this study took the medication, given that they reported clearer skin,
[tex]P(\frac{M}{C} ) = \frac{P(M\cap C)}{P(C)}[/tex]
⇒ [tex]P(\frac{M}{C} ) = \frac{0.15}{0.35}[/tex]
⇒ [tex]P(\frac{M}{C} ) = \frac{3}{7}[/tex]
⇒ [tex]P(\frac{M}{C} ) =0.42857142857\approx 0.43 [/tex]
Thus, [tex]P(\frac{M}{C} ) = 0.43[/tex] or [tex]43\%[/tex]
