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The question asks whether the given data represents a valid probability model. To determine this, we need to check two conditions for a probability model:

1. **All probabilities must be between 0 and 1.**
2. **The sum of all probabilities must equal 1.**

The given probabilities are:

- \( P(\text{HH}) = 0.15 \)
- \( P(\text{HT}) = 0.25 \)
- \( P(\text{TH}) = 0.06 \)
- \( P(\text{TT}) = 0.54 \)

Let's verify:

### Step 1: Check that all probabilities are between 0 and 1.
- \( 0.15 \), \( 0.25 \), \( 0.06 \), and \( 0.54 \) are all between 0 and 1, so this condition is satisfied.

### Step 2: Check if the sum of probabilities equals 1.
- \( 0.15 + 0.25 + 0.06 + 0.54 = 1.00 \)

Since the sum is exactly 1, the second condition is also satisfied.

### Conclusion:
Yes, the given data is a valid probability model.

Would you like any more details or have additional questions?

Here are 5 related questions to further your understanding:
1. How would you calculate the probability of getting at least one tail?
2. If the coin were fair, what would the probabilities for each outcome be?
3. How would you calculate the expected value for the number of heads in this case?
4. Can a probability model have values less than 0 or greater than 1?
5. How does this probability model differ from one representing a fair coin?

**Tip**: Always ensure the total of probabilities equals 1 when checking for a valid probability model.

Is the given table of probabilities a valid probability model?

Determine if the given probability table for coin toss outcomes (HH, HT, TH, TT) is a valid probability model by verifying that all probabilities sum to 1 and are between 0 and 1.

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