The pool of qualified jurors called for a highprofile case h

The pool of qualified jurors called for a high-profile case has 12 whites, 9 blacks, 4 Hispanics, and 2 Asians. From these, 12 will be selected to serve on the jury. Assume that all qualified jurors meet the criteria for serving. Find the probabilities of the following events. a No white is on the jury. b All nine blacks serve on the jury. C No Hispanics or Asians serve on the jury.

Solution

a. There are 27 of them.

15 are not whites. We pick 12 of them. That makes 15C12 possibilities = 455.

The total number of possible jurors is 27C12 = 17383860.

Thus, the said probability is 455/17383860 = 0.000026174. [ANSWER]

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B.

Thus, we choose 3 non-blacks out of 18. That\'s 18C3 possibilities = 816.

Thus,

p(all 9 blacks) = 816/17383860 = 0.00004694 [ANSWER]

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C.

Thus, we can choose on the 21 non-hispanic and asian.

That\'s 21C12 possibilities = 293930.

Thus, the said probability = 293930/17383860 = 0.016908 [ANSWER]