The following contingency table shows opinion about global warming (non-issue vs

Question

The following contingency table shows opinion about global warming (non-issue vs. serious concern) broken down by political party affiliation (Greens, Liberal and Labour). Answers may be fractions or decimals. a) What is the probability that an individual selected at random believes that global warming is a serious concern? b) What is the probability that an individual selected at random believes that global warming is a serious concern given that the individual is a Labour voter? c) Of the individuals who believe that global warming is a serious concern, what is the probability that the individual is a Labour voter? d) What type of probabilities did you find above? e) Is being a labour voter Independent from believing global warming is a serious issue? Explain your answer using probability.

Explanation / Answer

a)

Out of 1200 individuals there were 760 individuals who believe that global warming is a serious concern. Hence the required probability would be,

P = 760/1200 = 19/30

b)

Out of 200 labour voters there are 110 individual who belive that global warming is a serious concern. Hence the required probability would be given by,

P = 110/200 = 11/20

c)

Out of 760 individuals who believe that global warming is a serious concern there are 110 individuals who are labour voter. Hence the required probabiility would be given by,

P = 110/760 = 11/76

d)

The probabilities which we have found in the previous two parts here is conditional probability.

e)

If the probability that a labor voter who believes that global warming is a serious concern is equal to the product of probability that a random individual is a labour voter and the probability that an individual believes that global warming is a serious concern.

P(Labour)*P(Serious concern) = (200/1200)(760/1200) = 19/180

P(Labour voter and serious concern) =(110/1200) = 11/120

Since these two probabilities are not equal event of being a labour voter is independent of the event of believing that global warming is a serious concern.

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