Question: A new bill has been introduced in the House of Representatives. The composition of the House is \(46 \%\) Democrat and \(54 \%\) Republican. Of the representatives, \(27 \%\) support the bill, \(36 \%\) oppose the bill, and \(37 \%\) are undecided. Separately you are told that \(20 \%\) of Democrats strictly support the bill. You are also told that given that a representative is undecided, the probability that they are a Democrat is \(67.5 \%\)

1. Fill in the rest of the table.
2. What is the probability that a randomly selected representative is a Republican given that they strictly oppose the bill?
3. What is the probability that a randomly selected representative strictly opposes the bill given that they are a Republican?
4. You have shown that the probabilities in parts b) and c) are not equal. Does this imply dependence between the events in the rows and columns of the table? Explain why or why not.

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