A survey asked 1000 adults their support for a proposed new law. Each adult was

Question

A survey asked 1000 adults their support for a proposed new law. Each adult was asked whether they voted in the last election, those who had voted were classified as "Likely to vote". Those adults who had not voted were classified as "NOT likely to vote". Each adult was classified into one of 6 categories shown in the table below:

Find the probability a voter is Likely to Vote OR Favor the new law.

Note: Enter X.XX AT LEAST ONE DIGIT BEFORE THE DECIMAL, TWO AFTER and round up. Thus, 7 is entered as 7.0, 3.865 is entered as 3.87, 0.3750 is entered as 0.38

OpposeUndecidecd Likely to Vote NOT Likely to Vote Favor 372 151 87 25 262 103

Explanation / Answer

A: Event : Likely to Vote

B : Event : Favor the new Law

probability a voter is Likely to Vote OR Favor the new law = P(A or B)

By Addition theorem of probability

P( A or B) = P(A) + P(B) - P(A and B)

P(A) : Probability that voter likely to vote = Number of voters likely to vote / Total number of voters = 721/1000

P(B) : Probability that voter favor the new law = Number of voters favor the new law / Total number of voters = 523/1000

P(A and B) = Probability that voter likey to vote and favor the new law =

Number of voters likely vote and favor the new law / Total number of voters = 372/1000

Probability a voter is Likely to Vote OR Favor the new law = P(A or B)

P(A or B) = P(A) + P(B) - P(A and B) = 721/1000 + 523/1000 - 372/1000 = (721+523-372)/1000 = 872/1000 = 0.872

Probability a voter is Likely to Vote OR Favor the new law = 0.87

Favor oppose Undecided Total Likely to Vote 372 262 87 721 Not Likely To Vote 151 103 25 279 Total 523 365 112 1000

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