A committee of 6 is to review the value of wearing uniforms. The committee is to be chosen randomly from 5 interested teachers, the student council of 12 students and the 3 parents from the parent council. What are the following probabilities?
a) No students are on the committee
b) Has at leat 1 member from the parent council
+130511 A committee of 6 is to review the value of wearing uniforms. The committee is to be chosen randomly from 5 interested teachers, the student council of 12 students and the 3 parents from the parent council. What are the following probabilities?
a) No students are on the committee
We have 20 people and want to choose any 6 of them. The number of possible ways to do this = C(20,6) = 38760. So, no students on the committee means we want to choose any 6 people from the teachers' and parents' groups. And this can be done in C(8,6) = 28 ways. So, the probability of no students = 28 / 38760 = about .072%
b) Has at least 1 member from the parent council
This is just equal to 1 - probability of no members from the parent council. So we have
1 - C(17, 6)/C(20,6) = 1 - .319 = about .681 or 68.1%
+130511 A committee of 6 is to review the value of wearing uniforms. The committee is to be chosen randomly from 5 interested teachers, the student council of 12 students and the 3 parents from the parent council. What are the following probabilities?
a) No students are on the committee
We have 20 people and want to choose any 6 of them. The number of possible ways to do this = C(20,6) = 38760. So, no students on the committee means we want to choose any 6 people from the teachers' and parents' groups. And this can be done in C(8,6) = 28 ways. So, the probability of no students = 28 / 38760 = about .072%
b) Has at least 1 member from the parent council
This is just equal to 1 - probability of no members from the parent council. So we have
1 - C(17, 6)/C(20,6) = 1 - .319 = about .681 or 68.1%
