10. A school environment committee of
four people is to be selected from four
teachers and six grade 12 students.
a) What is the probability that the
committee is made up of two grade 12
students?
b) What is the expected number of
grade 12 students on the committee?



Answer :

Final answer:

This response explains how to calculate the probability of selecting a committee with two grade 12 students, as well as determining the expected number of grade 12 students on the committee.


Explanation:

A) To calculate the probability:

  1. Calculate the total number of ways to select a committee of 4 from 4 teachers and 6 students: 10 choose 4.
  2. Calculate the number of ways to have 2 grade 12 students and 2 others: 6 choose 2 * 4 choose 2.
  3. Divide the second result by the first to get the probability.

B) The expected number of grade 12 students on the committee can be found by multiplying the probability of having a grade 12 student by the total number of members.


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