1. **Problem Statement:** We have 13 jurors randomly selected from a population of 5 million residents, where 48% are minorities. Among the 13 jurors, 2 are minorities. 2. **Part (a): Find the proportion of the jury that is from a minority race.** The proportion is calculated as the number of minority jurors divided by the total number of jurors: $$\text{Proportion} = \frac{2}{13}$$ 3. **Calculate the value:** $$\frac{2}{13} \approx 0.1538$$ Rounded to two decimal places: $$0.15$$ 4. **Answer for (a):** The proportion of the jury from a minority race is approximately **0.15**. 5. **Part (b): Probability that 2 or fewer jurors are minorities when 13 are selected from a population with 48% minorities.** This is a binomial probability problem where: - Number of trials $n = 13$ - Probability of success (minority) $p = 0.48$ - We want $P(X \leq 2)$ where $X$ is the number of minority jurors. The binomial probability formula is: $$P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$$ We calculate: $$P(X \leq 2) = P(X=0) + P(X=1) + P(X=2)$$ 6. **Calculate each term:** $$P(X=0) = \binom{13}{0} (0.48)^0 (0.52)^{13} = 1 \times 1 \times 0.52^{13} \approx 0.00013$$ $$P(X=1) = \binom{13}{1} (0.48)^1 (0.52)^{12} = 13 \times 0.48 \times 0.52^{12} \approx 0.0019$$ $$P(X=2) = \binom{13}{2} (0.48)^2 (0.52)^{11} = 78 \times 0.2304 \times 0.52^{11} \approx 0.0109$$ 7. **Sum the probabilities:** $$P(X \leq 2) \approx 0.00013 + 0.0019 + 0.0109 = 0.0129$$ 8. **Answer for (b):** The probability that 2 or fewer jurors are minorities is approximately **0.013**. 9. **Part (c): What might the lawyer argue?** Since the expected proportion of minorities is 48%, but only 2 out of 13 jurors (about 15%) are minorities, which is much lower than expected, the lawyer might argue that the jury selection is not representative and possibly biased against minorities.