Question 1200420
**a) Probability of exactly three adults favoring the use of drones**

* This is a binomial probability problem. 

* **Formula:**
   P(X = k) = (nCk) * p^k * (1-p)^(n-k) 
   where:
       * n = number of trials (12 adults)
       * k = number of successes (3 adults favoring drone use)
       * p = probability of success (0.29)
       * (1-p) = probability of failure (0.71)
       * nCk = binomial coefficient (number of combinations of n items taken k at a time) 

* **Calculation:** 
   P(X = 3) = (12C3) * (0.29)^3 * (0.71)^(12-3) 
   P(X = 3) = 220 * 0.024389 * 0.040354 
   P(X = 3) ≈ 0.2173 

* **Probability of exactly three adults favoring the use of drones is approximately 0.2173 or 21.73%.**

**b) Probability of at least four adults favoring the use of drones**

* P(X ≥ 4) = P(X = 4) + P(X = 5) + ... + P(X = 12)

* This can be calculated using the binomial probability formula for each value of X from 4 to 12 and summing the probabilities. 

* **Alternatively, we can use the complement:**
   P(X ≥ 4) = 1 - P(X < 4) 
   P(X ≥ 4) = 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)]

* Calculate each of these probabilities using the binomial formula as in part (a).

* **Using a calculator or statistical software:** 
   P(X ≥ 4) ≈ 0.3205 

* **Probability of at least four adults favoring the use of drones is approximately 0.3205 or 32.05%.**

**c) Probability of less than eight adults favoring the use of drones**

* P(X < 8) = P(X = 0) + P(X = 1) + ... + P(X = 7)

* Calculate each of these probabilities using the binomial formula as in part (a).

* **Using a calculator or statistical software:**
   P(X < 8) ≈ 0.9589

* **Probability of less than eight adults favoring the use of drones is approximately 0.9589 or 95.89%.**

**Note:** These calculations can be performed using statistical software like R, Python (with libraries like SciPy or NumPy), or online calculators.