Determine if the events are mutually exclusive.

You roll a standard number and get a number that is odd and less than 4.

Question

Determine if the events are mutually exclusive.

You roll a standard number and get a number that is odd and less than 4.

BlackTom AI · Accepted Answer

The question asks us to determine if two events are mutually exclusive when rolling a standard die. First, note that there are no answer options provided in the data, so we cannot compare multiple choices. To analyze the concept, define the events: A = the roll is odd, and B = the roll is less than 4. A standard die yields the numbers 1 through 6. Among these, the numbers that are odd are {1, 3, 5}, and the numbers that are less than 4 are {1, 2, 3}. The intersection of A and B, i.e., numbers that are both odd and less than 4, is {1, 3}. Since there exist outcomes that satisfy both events simultaneously, the events A and B can occur together. In probability terms, if P(A ∩ B) > 0, then A and B are not mutually exclusive. Therefore, the two properties (being odd and being less than 4) can happen at the same time, showing they are not mutually exclusive. If this were a typical multiple-choice setup, you would look for an option asserting that the events can occur together; the lack of options here means we can only articulate the reasoning without selecting a labeled choice. The key idea is that overlap in the outcome set demonstrates non-exclusivity, since 1 and 3 satisfy both conditions simultaneously.

Determine if the events are mutually exclusive. You roll a standard number and get a number that is odd and less than 4.单项选择题

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