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Define the following events

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Please find the attached question.

Also, please see the formula sheet and standard normal distribution table to be used.

Only use a scientific or graphing calculator (Excel does not help me) and please show all working out.

Question 5

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.

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