You are driving home late one evening and listen to the end of the Washington Wizards game on the radio. You hear the announcer say: "Well, it's another day of DC fan magic! Earlier the Washington Capitals won and now the Wizards win! It seems everytime one of these teams wins, the other team wins as well!" As a statistician that makes you wonder, is this true? Are these two events actually dependent or independent? After the end of the season you collect the following information about the records of the two local teams (identifying a total of 82 "matched games."):
|
|
Washington Capitals (hockey)
|
|
|
|
|
WIN
|
LOSE (or TIE)
|
TOTAL
|
|
|
Washington
|
WIN
|
23
|
23
|
46
|
|
|
Wizards (basketball)
|
LOSE
|
22
|
14
|
36
|
|
|
TOTAL
|
45
|
37
|
82
|
|
|
|
|
|
|
|
Below is a table of joint and marginal probabilities based on the table above.
|
|
Washington Capitals (hockey)
|
|
|
|
WIN
|
LOSE (or TIE)
|
TOTAL
|
|
Washington
|
WIN
|
0.28
|
0.28
|
0.56
|
|
Wizards (basketball)
|
LOSE
|
0.27
|
0.17
|
0.44
|
|
TOTAL
|
0.55
|
0.45
|
1.00
|
Consider Event A to be "Capitals Win" and Event B to be "Wizards Win."
(a) What is P(A)? What is P(B)?
(b) Write out the formula/definition you will use to test whether these two events are independent.
(c) Use information from the table you created to make a decision about independence. What is your conclusion? Explain using specific numbers.