# Define the following events

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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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