What is the resulting sample space if
Two coins are tossed simultaneously ,

Answer

To find the resulting sample space when two coins are tossed simultaneously, we can follow these steps:

### Step 1: Identify the outcomes for each coin
When tossing a coin, there are two possible outcomes:
- Head (H)
- Tail (T)

### Step 2: Combine the outcomes of both coins
Since we are tossing two coins, we need to consider all combinations of the outcomes from the first and second coin.

1. The first coin can show Head (H) and the second coin can also show Head (H). This gives us the outcome (H, H).
2. The first coin can show Head (H) and the second coin can show Tail (T). This gives us the outcome (H, T).
3. The first coin can show Tail (T) and the second coin can show Head (H). This gives us the outcome (T, H).
4. The first coin can show Tail (T) and the second coin can also show Tail (T). This gives us the outcome (T, T).

### Step 3: List all possible outcomes
Now we can list all the outcomes we found:
- (H, H) - Both coins show Heads
- (H, T) - First coin shows Head, second coin shows Tail
- (T, H) - First coin shows Tail, second coin shows Head
- (T, T) - Both coins show Tails

### Step 4: Write the sample space
The sample space (S) is the set of all possible outcomes. Therefore, we can write:
\[ S = \{ (H, H), (H, T), (T, H), (T, T) \} \]

### Final Answer:
The resulting sample space when two coins are tossed simultaneously is:
\[ S = \{ (H, H), (H, T), (T, H), (T, T) \} \]

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