Question

A pool of potential jurors consists of 15 men and 13 women. 10 jurors are to be chosen at random from the pool of 28. 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? (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 9 men on the jury. Assuming the jury was chosen randomly, what is the chance of this occurring? P(9−men)= (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 9 men on the jury lead you to be suspicious about the randomness of the jury selection?

A. Yes, because the chance of 9 men being chosen on the jury is likely if the jury selection were random.

B. No, because the chance of 9 men being chosen on the jury is likely if the jury selection were random.

C. No, because the chance of 9 men being chosen on the jury is not likely if the jury selection were random.

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

Answer 1

here total number of ways selecting 10 jurors from the pool of 28 jurors is

a) Jury of exactly 3 men (7 women)

from 15 men chose 3 i.e

from 13 women chose 7 i.e.

Total ways from jury with 3 men and 7 women is 455*1716=780780

b) Half of the jury are men and half are women i.e 5 men and 5 women

Total ways to form 5 men and 5 women are 3003*1287=3864861

c) Jury of at least 2 women amongst 10 jurors

count the opposite case of 0 women or 1 woman

0 women i.e 10 men and 0 women

10 men=

1 woman i.e 9 men and 1 woman

9men=

1 woman=

Total ways to pick 0 women or 1 woman

=3003+5005*13

=3003+65065=68068 ways

Subtract this from total ways to get the ways to get 2 or more women

=13123110 - 68068

=13055042 ways

There fore