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The question provides the probabilities related to the next card being higher or lower after each card is turned over. Let’s analyze the situation step by step:

1. **After the first card is turned over**, the probability of the next card being lower is \( \frac{5}{6} \). 
   - This suggests that the first card must be very high, close to the highest possible number, so the majority of remaining cards are lower.
   - The only card that could make 5 out of the remaining 6 cards lower is **7**.

2. **After the second card is turned over**, the probability of the next card being higher is 80% (or \( \frac{4}{5} \)).
   - This implies that the second card is low, so most of the remaining cards are higher.
   - The card that makes 4 out of the remaining 5 cards higher is likely **1**.

3. **After the third card is turned over**, the probability that the next card is lower is 0.75 (or \( \frac{3}{4} \)).
   - This means the third card must be relatively high, so 3 of the 4 remaining cards are lower.
   - The card that fits this condition is **6**.

### Therefore, the first three cards in order are:
1. **7**
2. **1**
3. **6**

Would you like further details or explanations on how these probabilities were derived? 

Here are some related questions to expand your understanding:
1. How are probabilities calculated in this card guessing game?
2. What would the next card likely be after the third one (based on probabilities)?
3. How does each card reveal impact the remaining probabilities?
4. What would the situation look like if the second card was not the lowest?
5. How would the game change with more or fewer cards?

**Tip:** Understanding probability through practical scenarios like card games can help sharpen your intuition for predicting outcomes in complex situations.

7 cards, numbered from 1 to 7, are placed face down in a random order. The cards are turned over one by one. After each turn, I guess whether the next card will be higher or lower. After the first card has been turned over, the probability that the next card will be lower is 5/6. After the second card has been turned over, the probability that the next card will be higher is 80%. After the third card has been turned over, the probability that the next card will be lower is 0.75. What were the first three cards that were turned over? Write them in the order they were turned over.

Solve a probability puzzle involving 7 cards, where probabilities of the next card being higher or lower are given. This problem involves logical deduction and basic probability concepts, suitable for Grades 9-10.

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