Question

Franz and his friends are using the spinners below to play a game.

A spinner has 4 equal sections labeled 2, 4, 8, 6.

If one turn consists of spinning each spinner once, which table shows all the possible outcomes for one turn?
A 4-column table with 2 rows. The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2 A, 2 B. Column 2 has entries 4 A, 4 B. Column 3 has entries 6 A, 6 B. Column 4 has entries 8 A, 8 B.
A 4-column table with 3 rows. The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2 A, 2 B, 2 C. Column 2 has entries 4 A, 4 B, 4 C. Column 3 has entries 6 A, 6 B, 6 C. Column 4 has entries 8 A, 8 B, 8 C.
A 4-column table with 2 rows. The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2, A. Column 2 has entries 4, B. Column 3 has entries 6, C. Column 4 has entries 8, D.
A 4-column table with 3 rows. The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2 A, 2 A, 2 A. Column 2 has entries 4 B, 4 B, 4 B. Column 3 has entries 6 C, 6 C, 6 C. Column 4 has entries 8 A, 8 B, 8 C.

Answer 1

The correct answer is the first option. A 4-column table with 2 rows. The columns are labeled First Spinner and the rows are labeled Second spinner. Column 1 has entries 2 A, 2 B. Column 2 has entries 4 A, 4 B. Column 3 has entries 6 A, 6 B. Column 4 has entries 8 A, 8 B.

Explanation:

This table shows all the possible outcomes for one turn, because each cell represents a combination of the values from the first spinner and the second spinner. There are 4 possible values for the first spinner (2, 4, 6, or 8) and 2 possible values for the second spinner (A or B). Therefore, there are 4 x 2 = 8 possible outcomes in total, and each outcome has an equal probability of occurring.

The other options are incorrect because they do not show all the possible outcomes or they show duplicate outcomes. For example, the second option has 3 rows instead of 2, which implies that there are 3 possible values for the second spinner (A, B, or C), but this is not given in the question. The third option only shows one value for the second spinner for each column, which means it is missing half of the possible outcomes. The fourth option repeats the same value for the second spinner for each row, which means it is showing duplicate outcomes.