Challenging Questions

Mathematics – Compulsory Part

Learning Unit: More about probability

Question M0-16-01

There are \(200\) students in a school. Among them, \(84\) students are members of the Biology Club, while \(108\) students are members of the Chemistry Club. In addition, \(56\) students are members of both clubs. \(U\) is the set of all students in the school. \(B\) is the set of members of the Biology Club. \(C\) is the set of members of the Chemistry Club. The Venn diagram is as shown below:

1. Find \(n(U)\), \(n(B)\), \(n(C)\), \(n(B \cap C)\), \(n(B \setminus C)\), \(n(C \setminus B)\) and \(n(U \setminus (B \cup C))\).
2. If a student is chosen at random, what is the probability that he is a member of the Biology Club but not a member of the Chemistry Club? (Give the answer correct to 2 decimal places)
3. If a student is chosen at random, what is the probability that he is a member of the Chemistry Club but not a member of the Biology Club? (Give the answer correct to 2 decimal places)
4. If a member of the Biology Club is chosen at random, what is the probability that he is also a member of the Chemistry Club? (Give the answer correct to 2 decimal places)
5. If a member of the Chemistry Club is chosen at random, what is the probability that he is also a member of the Biology Club? (Give the answer correct to 2 decimal places)

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