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The problem you provided asks to find the probability of having "more than one fatal accident" during the next 100 million vehicular miles, given that the rate of fatal accidents is 1.32 per 100 million miles. This is a problem related to **Poisson distribution**, which is commonly used for modeling the probability of a given number of events happening in a fixed interval of time or space.

### Key Information:
- **Rate of occurrence (λ)** = 1.32 accidents per 100 million miles.
- **Interval length** = 100 million vehicular miles.
- We are tasked with finding the probability of **more than one** accident, which translates to finding \( P(X > 1) \).

### Steps to solve:

1. **Poisson distribution formula**:
   \[
   P(X = k) = \frac{{e^{-\lambda} \lambda^k}}{{k!}}
   \]
   where \( \lambda \) is the expected number of occurrences, and \( k \) is the number of events.

2. **Calculate \( P(X > 1) \)**:
   The probability of more than one accident is:
   \[
   P(X > 1) = 1 - P(X = 0) - P(X = 1)
   \]
   First, we calculate the probabilities of \( P(X = 0) \) and \( P(X = 1) \):

   - \( P(X = 0) = \frac{{e^{-\lambda} \lambda^0}}{{0!}} = e^{-\lambda} \)
   - \( P(X = 1) = \frac{{e^{-\lambda} \lambda^1}}{{1!}} = e^{-\lambda} \cdot \lambda \)

   For \( \lambda = 1.32 \):
   \[
   P(X = 0) = e^{-1.32} \approx 0.2673
   \]
   \[
   P(X = 1) = e^{-1.32} \cdot 1.32 \approx 0.3528
   \]

3. **Now, calculate**:
   \[
   P(X > 1) = 1 - P(X = 0) - P(X = 1)
   \]
   \[
   P(X > 1) = 1 - 0.2673 - 0.3528 = 0.3799
   \]

### Final Answer:
The probability that more than one fatal accident will occur is approximately **0.3799** (rounded to four decimal places).

Let me know if you would like more details or have any questions! Here are 5 related questions to explore further:

1. How does changing the accident rate affect the probability of multiple accidents?
2. What would the probability be for exactly two accidents?
3. Can we model this problem using a different distribution?
4. How do you compute the expected number of accidents in a longer distance interval?
5. How would the result change for a much smaller interval, such as 10 million miles?

**Tip**: The Poisson distribution is ideal for modeling rare events over a fixed interval, so it's great for situations like accident occurrences.

According to www.meretrix.com, traffic fatalities occur at the rate of 1.32 fatal accidents per 100 million miles. Find the probability that, during the next 100 million vehicular miles, there will be more than one fatal accident. Round your answer to FOUR decimal places.

Learn how to calculate the probability of having more than one fatal traffic accident in 100 million miles given a rate of 1.32 accidents per 100 million miles using the Poisson distribution. The detailed steps include the Poisson formula and cumulative probability, with answers rounded to four decimal places.

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