In A New Poll Regarding The Future Of The Canadian Senate

In A New Poll With Regard To The Future Of the Canadian Senate 70 Of

In a new poll regarding the future of the Canadian Senate, 70% of respondents expressed a desire to have a vote on the Senate’s future. Additionally, 50% of respondents favored abolishing the Senate, while 40% preferred to keep it as it currently is. The questions require analyzing probabilities related to these responses, including mutual exclusivity, independence, and conditional probabilities.

Paper For Above instruction

The Canadian Senate has been a subject of ongoing debate, reflecting diverse opinions about its role and future. Recent polling data provides valuable insights into public sentiment, revealing that a significant majority of respondents are interested in participating in a vote concerning the Senate’s future. The statistical analysis of these responses involves understanding concepts such as mutual exclusivity, independence, and conditional probabilities, which are foundational in probability theory and essential for interpreting survey data accurately.

Part A: Probability of Respondents Favoring Either Abolishing or Keeping the Senate

The first question explores the probability that a respondent belongs to either the group advocating for abolishing the Senate or the group favoring its current state, assuming these are mutually exclusive events. Mutually exclusive events cannot occur simultaneously; thus, their probabilities sum directly. Given that 50% of respondents favor abolition and 40% favor keeping the Senate, the probability that a randomly selected individual prefers either of these options is the sum of these probabilities:

P(abolish or keep) = P(abolish) + P(keep) = 0.50 + 0.40 = 0.90

This indicates a 90% chance that a randomly selected respondent falls into either of these two categories. It is important to recognize that these categories are mutually exclusive based on the problem statement, which allows us to simply add the probabilities without considering the intersection or overlaps.

Part B: Probability of Favoring Either Abolition or Voting for the Senate’s Future Assuming Independence

The second question involves a more complex scenario: assuming that the events "abolishing the Senate" and "voting for its future" are statistically independent, what is the probability that a respondent favors either of these outcomes? Independence implies that the occurrence of one event does not influence the probability of the other. The probability of the union of two independent events A and B is given by:

P(A or B) = P(A) + P(B) - P(A)×P(B)

From the first part, we know P(abolish) = 0.50. Additionally, since 70% of respondents desire a vote on the Senate’s future, P(vote) = 0.70. Assuming independence, the probability that a respondent favors either abolishing the Senate or voting for its future is:

P(abolish or vote) = 0.50 + 0.70 - (0.50 × 0.70) = 0.50 + 0.70 - 0.35 = 0.85

This result suggests an 85% probability that a respondent favors at least one of these options, reflecting the broad support for consultation or abolishment under the independence assumption.

Part C: Conditional Probability Involving Favoring the Senate and Voting on It

Lastly, the third question examines the probability that a respondent is either in favor of keeping the Senate or supports voting on its future, considering that 70% of those in favor of keeping the Senate wish to vote on it. The problem involves conditional probability: the likelihood of voting given support for keeping the Senate.

Given that 40% of respondents want to keep the Senate, and 70% of these favor voting, the probability that a randomly chosen respondent both favors keeping and votes on it is:

P(keep and vote) = P(keep) × P(vote | keep) = 0.40 × 0.70 = 0.28

Therefore, 28% of the respondents both favor preserving the Senate and support voting on its future. To find the probability that a respondent either favors keeping the Senate or votes on its future, we use the inclusion-exclusion principle:

P(keep or vote) = P(keep) + P(vote) - P(keep and vote) = 0.40 + 0.70 - 0.28 = 0.82

This indicates an 82% chance that a respondent either favors keeping the Senate or supports voting on its future, considering the conditional relationship.

Conclusion

The analysis of the survey data reveals significant support among respondents for actively participating in decisions about the Canadian Senate’s future. Under the assumptions of mutual exclusivity and independence, the probabilities demonstrate a broad consensus favoring either constitutional reform or maintaining the status quo through democratic processes. Furthermore, the conditional probability emphasizes that a majority of those favoring the Senate’s preservation are also inclined to vote on its future, underlining the importance of public engagement in constitutional matters.

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