Answer: a) 0.17, b) 0.0363
Step-by-step explanation:
Since we have given that
Number of jurors selected = 12
Number of minorities of jurors = 2
(a) What proportion of the jury described is from a minority race?
![\dfrac{2}{12}=\dfrac{1}{6}=0.166666\approx0.17](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B12%7D%3D%5Cdfrac%7B1%7D%7B6%7D%3D0.166666%5Capprox0.17)
(b) If 12 jurors are randomly selected from a population where 46% are minorities, what is the probability that 2 or fewer jurors will be minorities?
Let X be the number of jurors who are minorities.
Probability of getting minorities = 0.46
Probability of getting no minorities = 1-0.46 =0.54
![P(X\leq 2)=^{12}C_0(0.54)^{12}+^{12}C_1(0.46)(0.54)^{11}+^{12}C_2(0.46)^2(0.54)^{10}\\\\P(X\leq 2)=0.0363](https://tex.z-dn.net/?f=P%28X%5Cleq%202%29%3D%5E%7B12%7DC_0%280.54%29%5E%7B12%7D%2B%5E%7B12%7DC_1%280.46%29%280.54%29%5E%7B11%7D%2B%5E%7B12%7DC_2%280.46%29%5E2%280.54%29%5E%7B10%7D%5C%5C%5C%5CP%28X%5Cleq%202%29%3D0.0363)
(c) What might the lawyer of a defendant from this minority race argue?
Since the number of minorities juror are high among the population.
Hence, a) 0.17, b) 0.0363