Probability

Step 1: Understanding the Question: We are given data about a group of 50 people and the three medicines they received. We need to find the number of people who received at least two medicines. This means we need to find the number of people in the regions .

Step 2: Key Formula or Approach: We can use the Principle of Inclusion-Exclusion for three sets. Let's assume everyone received at least one medicine, so . The formula is: We want to find .
The number of people who received at least two medicines is given by:

Step 3: Detailed Explanation: Let's plug the given values into the Inclusion-Exclusion formula:
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• Let . Let:
= exactly A and B,
= exactly B and C,
= exactly A and C,
. Then:


So: Substitute : This is the number of people who received exactly two medicines.
Number of people who received at least two medicines:

Step 4: Final Answer:
The number of members who received at least two medicines is .