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

Options are : 1/20,19/20,37/40,3/40

To find the probability that the first house Maggie checks is not Tom's, let's analyze the problem step by step:

1. **Total Number of Houses in Each Lane:**  
   Maggie comes across 4 lanes, and there are 5 houses at the end of each lane. However, since she is checking just one house (the first one she checks), we'll focus on the probability for just one lane.

2. **Probability Calculation:**  
   In each lane, there are 5 houses, and only 1 of them is Tom's.  
   - The probability that Maggie randomly checks Tom's house first is \( \frac{1}{5} \).
   - Therefore, the probability that the first house Maggie checks is **not** Tom's is \( 1 - \frac{1}{5} = \frac{4}{5} \).

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

Let's compare this with the options provided:
- \(\frac{1}{20}\)
- \(\frac{19}{20}\)
- \(\frac{37}{40}\)
- \(\frac{3}{40}\)

Since \( \frac{4}{5} = \frac{4 \times 8}{5 \times 8} = \frac{32}{40} \), this value does not directly match any of the options. However, based on the logic provided:

- The correct answer should be the closest match, which is not directly listed.
  
Please check the problem statement or provided options as it might be a misprint or an error in the given choices. The expected probability, based on the problem's description, is \( \frac{4}{5} \) or \( \frac{32}{40} \), but none of the listed choices match exactly.

Would you like further details or have any questions? 

Here are some related questions:
1. What is the probability that Maggie checks Tom's house first?
2. How does the number of lanes affect the overall probability?
3. If Maggie checks one house from each lane, what is the probability that none of them are Tom's house?
4. What is the probability of Maggie finding Tom's house on the first try if she checks two houses per lane?
5. How does the problem change if there are 6 houses per lane?
6. What if Tom's house is always the first one? How does this change the problem?
7. How would the probabilities change if there were 10 houses per lane?
8. How can this probability problem be modeled using a simulation?

**Tip:** For problems involving probability, breaking the problem into smaller steps often clarifies the solution process.

Explore a probability problem involving finding Tom's house in a neighborhood with multiple lanes and houses. Learn how to calculate the probability that the first house Maggie checks is not Tom's. Suitable for Grades 7-9.

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