1. **Problem statement:** Destiny samples 4 products without replacement from a batch of 100 products, 14 of which are defective. We want to find the probability that all 4 sampled products are defective. 2. **Formula and rules:** The probability of selecting all defective products without replacement is given by the hypergeometric probability: $$P(\text{all defective}) = \frac{\binom{14}{4}}{\binom{100}{4}}$$ where $\binom{n}{k}$ is the binomial coefficient representing combinations. 3. **Calculate numerator:** Number of ways to choose 4 defective products from 14: $$\binom{14}{4} = \frac{14!}{4!(14-4)!} = \frac{14 \times 13 \times 12 \times 11}{4 \times 3 \times 2 \times 1} = 1001$$ 4. **Calculate denominator:** Number of ways to choose any 4 products from 100: $$\binom{100}{4} = \frac{100!}{4!(100-4)!} = \frac{100 \times 99 \times 98 \times 97}{4 \times 3 \times 2 \times 1} = 3,921,225$$ 5. **Calculate probability:** $$P = \frac{1001}{3,921,225} \approx 0.000255$$ 6. **Interpretation:** The probability that all 4 sampled products are defective is approximately 0.000255, which is very low. **Final answer:** $$\boxed{0.000255}$$