Question

(1 point) A pool of potential jurors consists of 16 men and 14 women. 10 jurors are to be chosen at random from the pool of 30. What is the probability that this jury is made up Part (a) 3 men? Part (b) half of the jury are men and half are women? Part (c) at least two women are amongst the 10 jurors? EEE (use four decimals) (use four decimals) (use four decimals) Part (d) The jury has been selected and there are 9 men on the jury. Assuming the jury was chosen randomly, what is the chance of this occurring? P(9-men) = Part (e) Consider the jury selection that occurred in part (d) and the probability this happening. Would you this particular jury cause you to question the randomness of the jury selection? That is, can the 9 men on the jury lead you to be suspicious about the randomness of the jury selection? E (use four decimals) A. No, because the chance of 9 men being chosen on the jury is likely if the jury selection were random. B. Yes, because the chance of 9 men being chosen on the jury is not likely if the jury selection were random. C. Yes, because the chance of 9 men being chosen on the jury is likely if the jury selection were random. D. No, because the chance of 9 men being chosen on the jury is not likely if the jury selection were random.

Answer 1

(a) P ( 3 men ) = ¹⁶C_{3 .} ¹⁴C_7. /³⁰C₁₀ = 560*3432/ 30045015 = 0.0640

(b) P ( 5 men , 5 women ) = ¹⁶C_{5 .} ¹⁴C_5. /³⁰C₁₀ = 0.2911   

(c) P ( atleast 2 women) = 1- P ( atmost 1 women) = 1- [ ¹⁶C_{10 .} ¹⁴C_0. /³⁰C₁₀ + ¹⁶C_{9 .} ¹⁴C_1. /³⁰C₁₀ ] = 0.9944

(d) P ( 9 men) = ¹⁶C_{9 .} ¹⁴C_1. /³⁰C₁₀ = 0.0053   

(e)B. Yes, because the chance of 9 men being chosen on the jury is not likely if the jury selection were random