Challenging Questions

Mathematics – Compulsory Part

Learning Unit: More about probability

Question M0-16-02

There are \(50\) teachers in a school. Among them, \(30\) teachers are male, while \(20\) teachers are female. In addition, \(8\) English teachers are male and \(5\) English teachers are female. A school committee of \(4\) teachers is formed by selecting them at random.

1. Using the concept of multiplication law of probability, calculate the probability that the committee consists entirely of all male teachers. (Give the answer correct to 4 decimal places)
2. Using the concept of combinations, calculate the probability that the committee consists entirely of all female teachers. (Give the answer correct to 4 decimal places)
3. Using the concept of multiplication law of probability, calculate the probability that the committee consists of at least \(2\) English teachers. (Give the answer correct to 4 decimal places)
4. Using the concept of combinations, calculate the probability that the committee includes at least one male teacher and at least one female teacher. (Give the answer correct to 4 decimal places)
5. Verify the answer in (4) using the results of (1) and (2).

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