Question
Jill has two dimes she is going to use to perform a probability experiment. What will the sample space look like if she flips the two dimes simultaneously?
Answers
GPT-4o mini
When Jill flips two dimes simultaneously, each dime can land in one of two positions: heads (H) or tails (T). To determine the sample space, we can list all the possible outcomes based on the two dimes.
The possible outcomes are:
1. Both dimes show heads: (H, H)
2. The first dime shows heads and the second dime shows tails: (H, T)
3. The first dime shows tails and the second dime shows heads: (T, H)
4. Both dimes show tails: (T, T)
Thus, the sample space \( S \) can be represented as follows:
\[ S = \{ (H, H), (H, T), (T, H), (T, T) \} \]
This means that there are a total of 4 possible outcomes when flipping the two dimes.
The possible outcomes are:
1. Both dimes show heads: (H, H)
2. The first dime shows heads and the second dime shows tails: (H, T)
3. The first dime shows tails and the second dime shows heads: (T, H)
4. Both dimes show tails: (T, T)
Thus, the sample space \( S \) can be represented as follows:
\[ S = \{ (H, H), (H, T), (T, H), (T, T) \} \]
This means that there are a total of 4 possible outcomes when flipping the two dimes.