Question

A committee of four students will be selected from a list that contains six Grade 9 students and eight Grade 10 students.

a) Show the probability distribution for the number of grade 10's on the committee.

b) What is the expected number of Grade 10 students on the committee?

Answer 1

Let X be the number of grade-10 students. One selection cannot be done more than once, so we are choosing without replacement hence X is hypergeometrically distributed because

a) There will be several cases :

• 0 grade-10 student = P(X=0) = 6C4 *8C0/ 14C4 = 0.0149

• 1 grade-10 student = P(X=1) = 6C3*8C1/14C4 = 0.1598

• 2 grade-10 students = P(X=2) = 6C2*8C2/14C4 = 0.4195

• 3 grade-10 students = P(X=3) = 6C1*8C3/14C4 = 0.3356

• 4 grade-10 students = P(X=4) = 6C0*8C4/14C4 = 0.0699

This will be the probability distribution of number of grade 10's on the committee. We can plot these points on graph to visualise distribution.

b) For hypergeometric distribution HYP(n,M,N)

n: The number of items in the sample,

M: The number of items in the population that are classified as successes,

N: The number of items in the population

the mean of distribution is given by n*M/N = 4*8/14 = 2.285 .