1. **State the problem:** Find the probability that a baseball player with a batting average of 0.28 hits exactly 4 times in 12 at-bats. 2. **Formula used:** This is a binomial probability problem. The formula is: $$P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$$ where: - $n$ is the number of trials (at-bats), - $k$ is the number of successes (hits), - $p$ is the probability of success on a single trial, - $\binom{n}{k}$ is the binomial coefficient. 3. **Calculate the binomial coefficient:** $$\binom{12}{4} = \frac{12!}{4! (12-4)!} = \frac{12!}{4! 8!}$$ 4. **Calculate the probability:** $$P(X=4) = \binom{12}{4} (0.28)^4 (0.72)^8$$ 5. **Intermediate calculation:** Calculate $\binom{12}{4}$: $$\binom{12}{4} = \frac{12 \times 11 \times 10 \times 9}{4 \times 3 \times 2 \times 1} = \frac{11880}{24} = 495$$ 6. **Substitute values:** $$P(X=4) = 495 \times (0.28)^4 \times (0.72)^8$$ 7. **Calculate powers:** $$ (0.28)^4 = 0.0061477 \quad \text{(approx)}$$ $$ (0.72)^8 = 0.0587197 \quad \text{(approx)}$$ 8. **Multiply all:** $$P(X=4) = 495 \times 0.0061477 \times 0.0587197 \approx 495 \times 0.0003609 = 0.1786$$ 9. **Final answer:** The probability that the player hits exactly 4 times in 12 at-bats is approximately **0.18**. --- 10. **Next problem:** Explain the "N" in BINS for the same scenario. 11. **Explanation:** In BINS (Binomial setting), "N" represents the number of trials or attempts. 12. **In this problem:** The player is at bat 12 times, so $N=12$. 13. **Answer:** The correct statement is: **He is at bat 12 times**.