Question 1090706: The manager of Ardmore Pharmacy knows that 25% of the customers entering the store buy prescription drugs, 65% buy over-the-counter drugs and 18% buy both types of drugs. What is the probability that a randomly selected customer will buy at least one of these two types of drugs?
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website! Question:
The manager of Ardmore Pharmacy knows that 25% of the customers entering the store buy prescription drugs, 65% buy over-the-counter drugs and 18% buy both types of drugs. What is the probability that a randomly selected customer will buy at least one of these two types of drugs?
Solution:
METHOD A
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Step 1:
Draw a Venn diagram with two overlapping circles A & B.
Label A with 65%, and B with 25%.
The overlapped area is 18%.
Step 2:
Calculate the percentage of the total area covered by the two circles, noting that
- Non-overlapping area of A = 65-18=47%
- non-overlapping area of B = 25-18=7%
Step 3:
Interpret and conclude the total area covered by A & B, meaning the total percentage covered represents the percentage of customers who buy either prescription or over-the-counter (OTC) drugs, or both.
Method B:
Use the relationship between union and intersection of two sets:
P(A∪B)=P(A)+P(B)-P(A∩B)=65%+25%-18%=72%
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