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?
The multiplication principle should be used to determine the possible voting outcomes.
In this scenario, the multiplication principle applies because each of the eight voters can choose from three candidates independently. Therefore, the total number of possible voting outcomes can be calculated by multiplying the number of choices each voter has, which is a direct application of the multiplication principle in combinatorial counting.
Combinations are used when the order of selection does not matter, such as when choosing a subset of items from a larger set without regard to arrangement. In this case, since each voter is making an independent choice among candidates, the order in which votes are cast is significant, making combinations inappropriate for this scenario.
Bayes' theorem is a method for updating probabilities based on new evidence and is primarily applied in conditional probability scenarios. Since the question does not involve updating probabilities based on prior outcomes but rather calculating the total number of outcomes, Bayes' theorem is not relevant here.
Conditional probability deals with the likelihood of an event occurring given that another event has already occurred. Since the voting is independent for each voter, and we are not conditioning on previous votes or outcomes, this concept does not apply to determining the total possible voting outcomes.
The multiplication principle states that if one event can occur in 'm' ways and a second can occur independently in 'n' ways, the two events can occur in m × n ways. Here, as each of the eight voters selects from three candidates independently, the total outcomes can be calculated as 3^8, illustrating the correct application of this principle.
In summary, the multiplication principle is the correct statistical rule for determining possible voting outcomes when each voter independently chooses among multiple candidates. This principle allows us to calculate the total number of combinations of votes effectively, demonstrating its applicability in straightforward voting scenarios.
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