5.2-07 – Introductory Statistics – Sheldon M. Ross

Question:

Two volleyball teams are to play a 2-out-of-3 series, in which they continue to play until one has won 2 games. Suppose that the home team wins each game played, independently, with probability 0.7. Let X denote the number of games played.

(a)            What are the possible values of X?

(b)           What is the probability distribution of X?

Solution:

Let X = the number of games played

Game 1	Game 2	Game 3	X	P (Win) by Home team	P (Win) by Visiting team	Total P(Win)
W	W	-	2	(0.7)2 = 0.490	(0.3)2 = 0.090	0.580
W	L	W	3	(0.3) (0.7)2 = 0.147	(0.7) (0.3)2 = 0.063	0.210
L	W	W	3	(0.3) (0.7)2 = 0.147	(0.7) (0.3)2 = 0.063	0.210
Total				0.784	0.216	1.000

Answer (a):

The possible values that X can take are:

·        2

·        3

Answer (b):

Let X = the number of games played

Probability distribution of X is as below

X	P (X)
2	0.58
3	0.42
	1.00