Tom invites Maggie for a party Maggie knows that on her way to Tom's house, she will come across 4 lanes. There are 5 houses at the end of each lane One of the those houses is Tom's . What is the probability that the first house that Maggie checks is  s not Tom's?

To solve this problem, we need to determine the probability that the first house Maggie checks is **not** Tom's house.

### Step 1: Analyze the Problem
- There are 4 lanes, and each lane has 5 houses.
- We are interested in the probability that the first house Maggie checks is not Tom's.

### Step 2: Calculate the Probability
- For any given lane, there is 1 house that belongs to Tom out of the 5 houses.
- Therefore, the probability that Maggie checks Tom's house first is \( \frac{1}{5} \).
- Consequently, the probability that she does **not** check Tom's house first is the complement of this probability.

\[
\text{Probability that the first house checked is not Tom's} = 1 - \frac{1}{5} = \frac{4}{5}
\]

### Final Answer:
The probability that the first house Maggie checks is not Tom's is \( \frac{4}{5} \) or 0.8.

Would you like more details, or do you have any further questions?

Here are some related questions:
1. What is the probability that Maggie checks Tom's house second?
2. How would the probability change if there were 6 houses in each lane instead of 5?
3. What is the probability that Maggie checks Tom's house after checking two other houses?
4. How does the probability change if Tom's house is located in a random lane?
5. What is the probability that Maggie finds Tom's house within two checks?
6. If Maggie randomly chooses a lane, what is the probability she picks the lane where Tom's house is?
7. What is the probability that the first house Maggie checks in each lane is not Tom's?
8. How would the probability change if there were 10 houses in each lane instead of 5?

**Tip:** When solving probability problems, consider both the favorable outcomes and the total possible outcomes to understand the scenario fully.

Explore a probability problem involving finding Tom's house among multiple lanes and houses. Calculate the probability that the first house Maggie checks is not Tom's using the complement rule. Suitable for students in Grades 7-9.

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