12-A pool of potential jurors consists of 16 men and 15 women. 10 jurors are to

Question

12-A pool of potential jurors consists of 16 men and 15 women. 10 jurors are to be chosen at random from the pool of 31.

What is the probability that this jury is made up

Part (a) 2 men? (use four decimals)

Part (b) half of the jury are men and half are women? (use four decimals)

Part (c) at least two women are amongst the 10 jurors? (use four decimals)

Part (d) The jury has been selected and there are 10 men on the jury. Assuming the jury was chosen randomly, what is the chance of this occurring?
P(10men)=P(10men)= (use four decimals)

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 10 men on the jury lead you to be suspicious about the randomness of the jury selection?
A. Yes, because the chance of 10 men being chosen on the jury is not likely if the jury selection were random.
B. No, because the chance of 10 men being chosen on the jury is likely if the jury selection were random.
C. Yes, because the chance of 10 men being chosen on the jury is likely if the jury selection were random.
D. No, because the chance of 10 men being chosen on the jury is not likely if the jury selection were random.

Explanation / Answer

A) P(2 men) = P(2 men from 16 and 8 women from 15)

= 16C2x15C8/31C10

= 0.0174

b) P(half women and half men) = P(5 men and 5 women)

= 16C5x15C5/31C5

= 0.2957

C) P(at least 2 women) = P(0 men) + P(1 man) + P(2 men)

= 15C10/31C10 + 16C1x15C9/31C10 + 16C2x15C8/31C10

= 0.0001 + 0.0018 + 0.0174

= 0.0193

D) P(10 men) = 16C10/31C10

= 0.0002

E) A. Yes, because the chance of 10 men being chosen on the jury is not likely if the jury selection were random.

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