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List all the elements of the sample space for the following experiment:

You spin a spinner with four equal sections labeled 1, 2, 3, and 4, and toss a dime.

A. (1, H), (2, H), (3, H), (4, H), (1, H), (2, H), (3, H), (4, H)
B. (1, H), (2, H), (3, H), (4, H), (1, T), (2, T), (3, T), (4, T)
C. (1, T), (2, T), (3, T), (4, T), (1, T), (2, T), (3, T), (4, T)
D. (1, H), (H, 1), (2, H), (H, 2), (3, H), (H, 3), (4, H), (H, 4), (1, T), (2, T), (3, T), (4, T)

Please select the best answer from the choices provided.



Answer :

GinnyAnswer
To determine the elements of the sample space for the experiment where you spin a spinner with four equal sections labeled 1, 2, 3, and 4 and toss a dime, we need to list all possible outcomes of the combined events.

The spinner can land on 1, 2, 3, or 4, and the dime can land on either Heads (H) or Tails (T). Therefore, the possible outcomes can be represented as ordered pairs where the first element is the result of the spinner and the second element is the result of the dime.

1. If the spinner lands on 1, the possible outcomes for the dime are:
- (1, H)
- (1, T)

2. If the spinner lands on 2, the possible outcomes for the dime are:
- (2, H)
- (2, T)

3. If the spinner lands on 3, the possible outcomes for the dime are:
- (3, H)
- (3, T)

4. If the spinner lands on 4, the possible outcomes for the dime are:
- (4, H)
- (4, T)

Combining these, we get the full sample space:
- (1, H)
- (2, H)
- (3, H)
- (4, H)
- (1, T)
- (2, T)
- (3, T)
- (4, T)

Thus, the correct answer is (b):
- (1, H), (2, H), (3, H), (4, H), (1, T), (2, T), (3, T), (4, T)

The total number of outcomes in the sample space is 8. Therefore, the sample space contains 8 elements.

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