To determine which events belong to the sample space for Trevor's spins on the spinners, let's first identify the possible outcomes for each spinner based on the numbers you're given:
Left Spinner outcomes: 4, 9, 4, 2, 2, 9, 9, 5, 1, 3
(Unique outcomes: 1, 2, 3, 4, 5, 9)
Right Spinner outcomes: 4, 9, 4, 2, 2, 9, 9, 5, 1, 3
(Unique outcomes: 1, 2, 3, 4, 5, 9)
Now let's analyze the options:
(a) (2, 2) - This is possible since both spinners can result in 2.
(b) (3, 3) - This is possible since both spinners can result in 3.
(c) (even number, odd number) - This is possible as the left spinner can yield an even number (2, 4) and the right spinner can yield an odd number (1, 3, 5, 9).
(d) (2, 1) - This is possible since the left spinner can yield 2 and the right spinner can yield 1.
(e) (1, 5) - This is possible since the left spinner can yield 1 and the right spinner can yield 5.
(f) (odd number, odd number) - This is possible as both spinners can yield odd numbers (1, 3, 5, 9).
(g) (9, 9) - This is possible since both spinners can result in 9.
(h) (even number, even number) - This is possible as both spinners can yield even numbers (2, 4).
Now let's match these findings with the options provided:
- A: a, b, c, d - All valid.
- B: c, d, f, g - All valid.
- C: c, d, g, h - All valid.
- D: a, c, d, g - All valid.
Since many of these selections are valid, we need to choose an option that includes only valid events from the listed choices.
Given that all of the letters refer to valid outcomes, the correct answer could be any of these options as they all contain valid pairs according to the sample space provided.
If you want to select the most inclusive option, B (c, d, f, g) appears to cover a wide range of valid conditions (including even/odd and odd/odd as well as a specific occurrence of the number 9), thus it could be considered most representative of the diversity in the sample space. Therefore, the answer would be:
B. c, d, f, g.