Question 10

The sample space for this experiment is {A, B, C, D}.

The sample space consists of all possible outcomes of the experiment, which in this case includes the four labeled sections of the spinner: A, B, C, and D.

A) {A, B, C, D, E}

This option is incorrect because it includes an extra element, E, which is not part of the spinner's sections. The sample space must only contain the outcomes represented by the sections on the spinner.

B) {1, 2, 3, 4}

This option is also incorrect as it uses numerical labels instead of the actual labels of the spinner's sections. The sample space should reflect the specific outcomes of the experiment, which are represented by letters A, B, C, and D.

C) {A, B, C, D}

This option is correct because it accurately lists all the possible outcomes of the spinner experiment. The sample space must include each section that can be landed on when the spinner is spun.

D) {AB, CD}

This option is incorrect as it combines outcomes into pairs rather than listing them individually. The sample space must represent each individual section of the spinner, not combinations of sections.

Conclusion

The correct answer, {A, B, C, D}, clearly defines the sample space by including each distinct outcome represented on the spinner. All other options fail either by including irrelevant outcomes, using incorrect labels, or misrepresenting the nature of the sample space by combining outcomes. Thus, C is the only accurate representation of the spinner's sections.