Discuss the below:
Q: A random sample of 1000 voters was cross-classified according to income level and the political party they plan to vote for in an upcoming election. The results were as follows:
|
Income
|
Liberal
|
Conservative
|
NDP
|
Total
|
|
|
(LIB)
|
(CON)
|
(NDP)
|
|
|
High (H)
|
110
|
250
|
0
|
360
|
|
Middle (M)
|
300
|
140
|
20
|
460
|
|
Low (L)
|
60
|
100
|
20
|
180
|
|
Total
|
470
|
490
|
40
|
1000
|
One voter is selected at random.
Define the following events:
H = voter selected has a high income
M = voter selected has a middle income
L = voter selected has a low income
LIB = voter selected plans to vote Liberal
CON = voter selected plans to vote conservative
NDP = voter selected plans to vote NDP
a. What is the probability that the selected voter
i. plans to vote Liberal or has a middle income?
ii. plans to vote NDP given that he or she has a low income?
iii. has a high income and plans to vote conservative?
b. Are the events "M" and "CON"
i. mutually exclusive? Explain.
ii. independent? Show your proof.
Attachment:- table.rar