A local ice cream shop offers three flavors: vanilla, chocolate, and strawberry. A customer can choose only one flavor for their single-scoop cone. Based on this scenario, which of the following statements is true?

Question

BlackTom AI · Accepted Answer

Begin by restating the scenario: a local ice cream shop offers three flavors—vanilla, chocolate, and strawberry—and a customer can choose only one flavor for their single-scoop cone. Now evaluate each option in light of this setup.
Option 1: 'Choosing strawberry and not choosing strawberry are mutually inclusive events.' This is incorrect. In probability terms, 'choosing strawberry' and 'not choosing strawberry' are direct opposites; they cannot occur together, so they are mutually exclusive, not mutually inclusive. The statement also uses 'mutually inclusive,' which is not standard terminology for this context and is misleading.
Option 2: 'Choosing all three flavors is possible in a single scoop.' This is false because the scenario specifies a single-scoop cone, meaning only one flavor can be selected. Since there are three flavors available, selecting all three in one scoop is logically impossible.
Option 3: 'Choosing vanilla and chocolate are mutually exclusive events.' This is true. With only one scoop, you cannot simultaneously choose both vanilla and chocolate; selecting one flavor excludes the other. Thus, the events of choosing vanilla and choosing chocolate cannot occur together, satisfying mutual exclusivity.
Option 4: 'The probability of choosing vanilla or chocolate is always 1.' This is incorrect. Since there are three flavors and only one will be chosen, the probability of selecting vanilla or chocolate is not guaranteed to be 1; it depends on the probability distribution over the flavors. If we assumed equal likelihood for each flavor, the probability would be 2/3, not 1. More generally, the probability of vanilla or chocolate is not universally 1 unless one of the flavors had probability 0 and the other 1, which is not specified here.
In summary, the only statement that aligns with a single-scoop choice among three flavors is that vanilla and chocolate are mutually exclusive events, while the other statements contradict the single-scoop constraint or misstate probability implications.

A local ice cream shop offers three flavors: vanilla, chocolate, and strawberry. A customer can choose only one flavor for their single-scoop cone. Based on this scenario, which of the following statements is true?单项选择题

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