Question 1199410
**a) Probability of Exactly Seven Deaths**

* **Poisson Distribution Formula:**
   P(X = k) = (λ^k * e^(-λ)) / k! 
   where:
       * X is the number of occurrences (deaths)
       * λ is the average number of occurrences (10)
       * k is the specific number of occurrences (7)
       * e is the base of the natural logarithm (approximately 2.71828)

* **Calculate:**
   P(X = 7) = (10^7 * e^(-10)) / 7! 
   P(X = 7) ≈ 0.0901

* **Probability of exactly seven deaths: 0.0901 or 9.01%**

**b) Probability of Ten or More Deaths**

* **Calculate the probability of fewer than ten deaths:**
   P(X < 10) = P(X = 0) + P(X = 1) + ... + P(X = 9) 

   * Calculate each probability using the Poisson formula as in part (a).

* **Probability of ten or more deaths:**
   P(X ≥ 10) = 1 - P(X < 10) 

* **Using a Poisson probability table or calculator:**
   P(X ≥ 10) ≈ 0.5830

* **Probability of ten or more deaths: 0.5830 or 58.30%**

**Note:**

* You can use statistical software (like R, Python, or Excel) or online calculators to calculate Poisson probabilities more efficiently.
* The Poisson distribution assumes that events are independent and occur at a constant average rate.