Question 33

The multiplication principle should be used to determine the possible voting outcomes.

In this scenario, the multiplication principle is applicable as it allows for calculating the total number of possible outcomes when each voter can independently choose one candidate from three options.

A) Combination

The combination method is incorrect as it is used to determine the number of ways to choose a subset of items from a larger set without regard to the order of selection. In this case, we are interested in the total number of outcomes from multiple independent votes, not selecting candidates.

B) Bayes' theorem

Bayes' theorem is not applicable here, as it is used to update the probability of a hypothesis based on new evidence. The voting scenario does not involve conditional probabilities that would require prior information about the candidates or voters' preferences.

C) Conditional probability

Conditional probability is also inappropriate for this context because it deals with the likelihood of an event occurring given that another event has already occurred. This voting scenario does not depend on prior events or conditions but rather on independent voting choices.

D) Multiplication principle

The multiplication principle is the correct approach because it states that if one event can occur in 'm' ways and a second can occur independently in 'n' ways, then the two events can occur in m * n ways. Here, each of the eight voters can independently choose one of three candidates, leading to a total of 3^8 possible outcomes.

Conclusion

The multiplication principle is the definitive method for determining the voting outcomes in this scenario, as it effectively accounts for the independent choices made by each voter. Other options such as combination, Bayes' theorem, and conditional probability do not apply to the independent nature of the voting process, making them unsuitable for this problem.