39. A political ballot gives voters the option to vote for one of three candidates. Eight voters cast their ballots. Which statistical rule should be used to determine the possible voting outcomes?
Answer: B
The multiplication principle should be used to determine the possible voting outcomes.
In this scenario, the multiplication principle is applicable as it allows us to calculate the total number of outcomes when there are multiple independent choices. Each voter has three options, and with eight voters, the multiplication principle facilitates determining the total combinations of votes.
A) Conditional probability
Conditional probability is not suitable in this context as it involves calculating the probability of an event given that another event has occurred. The question does not present a scenario where outcomes depend on previous votes or events, making this option incorrect.
B) Multiplication principle
The multiplication principle is the correct choice because it applies to situations where there are multiple independent choices. Each of the eight voters can select from three candidates, leading to \(3^8\) possible voting combinations, which is a direct application of the multiplication principle.
C) Combination
Combination is not the correct choice here because it involves selecting items from a larger set without regard to the order of selection. Since the ballot allows each voter to vote independently for one of three candidates, the focus is on the total number of possible outcomes rather than selecting a subset of candidates.
D) Bayes’ theorem
Bayes' theorem is irrelevant in this situation as it focuses on updating probabilities based on new evidence. The voting scenario does not involve prior probabilities or conditions altering the likelihood of outcomes, making this option incorrect.
Conclusion
The multiplication principle is definitively the correct choice for determining the possible voting outcomes, as it effectively accounts for the independent choices of each voter. Other options, such as conditional probability, combinations, and Bayes’ theorem, do not apply to the structure of the voting scenario and therefore fail to provide a relevant statistical framework for this question.