To determine which events are part of the sample space for Trevor's spins on the two spinners, we first need to identify the values on each spinner.
Given:
-
The left spinner consists of: 4, 1, 4, 6, 6, 1, 1, 7, 3, 5
- Unique values: 1, 3, 4, 5, 6, 7
-
The right spinner also has the same set of values.
From this, we can construct the possible events from both spinners. Each event should consist of two values (one from each spinner).
Now, let's analyze the provided options:
- (6, 6): Both spinners can show 6. Yes, this is part of the sample space.
- (3, 5): The left spinner can show 3 and the right spinner can show 5. Yes, this is part of the sample space.
- (even number, odd number): This is a category, where it indicates that one spinner shows an even number (4 or 6) and the other shows an odd number (1, 3, 5, 7). Yes, this is part of the sample space, as there are combinations that fulfill these conditions.
- (6, 3): The left spinner can show 6 and the right spinner can show 3. Yes, this is part of the sample space.
- (1, 7): The left spinner can show 1 and the right spinner can show 7. Yes, this is part of the sample space.
- (odd number, odd number): This indicates that both spinners show odd numbers. Yes, this is part of the sample space, as there are combinations that fulfill these conditions.
- (1, 1): Both spinners can show 1. Yes, this is part of the sample space.
- (even number, even number): This indicates that both spinners show even numbers. Yes, this is part of the sample space, as there are combinations that fulfill these conditions.
Now, looking at the options:
A. (a, c, d, g)
- a (6, 6) - YES
- c (even number, odd number) - YES
- d (6, 3) - YES
- g (1, 1) - YES
All included!
B. (c, d, g, h)
- c (even number, odd number) - YES
- d (6, 3) - YES
- g (1, 1) - YES
- h (even number, even number) - YES
All included!
C. (c, d, f, g)
- c (even number, odd number) - YES
- d (6, 3) - YES
- f (odd number, odd number) - YES
- g (1, 1) - YES
All included!
D. (a, b, c, d)
- a (6, 6) - YES
- b (3, 5) - YES
- c (even number, odd number) - YES
- d (6, 3) - YES
All included!
Since all options A, B, C, and D comprise events that are indeed part of the sample space, the most comprehensive collection of sample events includes A, B, C, and D.
However, the only option that is provided in a captivating way and explicitly shows unique combinations is:
- A. (a, c, d, g) which includes specific pairings and covers the essence of combinations possible from Trevor's spins.
Thus the most suitable answer is A.