Question

Noah randomly chooses four people to be on his basketball team from a group of 12 people (seven in grade 11, five in grade 12).

a. The random variable is the number of grade 12s on his team. Determine P(0) and explain what it means.

b. Create a probability distribution table and histogram for the number of grade 12s on his team.

c. What is the expected number of grade 12s on the team?

Answer 1

(a) Probability of the number of grade 12s = 5/12 = 0.42

P(0) = (1 - 0.42)^4 = 0.1158

(b) The probability distribution table is:

	12	n
	0.4167	p
		cumulative
X	P(X)	probability
0	0.00155	0.00155
1	0.01331	0.01486
2	0.05227	0.06713
3	0.12446	0.19160
4	0.20003	0.39163
5	0.22861	0.62023
6	0.19050	0.81074
7	0.11664	0.92737
8	0.05207	0.97944
9	0.01653	0.99597
10	0.00354	0.99951
11	0.00046	0.99997
12	0.00003	1.00000
	1.00000

The histogram for the number of grade 12s is:

(c) Expected number = 12*0.4167 = 5