At a conference promoting excellence in education for African Americans in Detro

Question

At a conference promoting excellence in education for African Americans in Detroit, special-edition books were selected to be given away in contests. There were 9 books written by Author A, 5 books by Author B, and 8 books by Author C. The judge of one contest selected 7 books at random for prizes. Find the probabilities that the selected consisted of the following. Complete parts (a) through (f) below.

a. 2 Author A books and 5 Author C books. (Type an integer or decimal rounded to four decimal places as needed.)

b. Exactly 4 Author B books. (Type an integer or decimal rounded to four decimal places as needed.)

c. 3 Author A, 3 Author B, and 1 Author C book. (Type an integer or decimal rounded to four decimal places as needed.)

d. At least 5 Author A books. (Type an integer or decimal rounded to four decimal places as needed.)

e. Exactly 4 books written by males (Authors A and B are male and Author C is female). (Type an integer or decimal rounded to four decimal places as needed.)

f. No more than 2 books written by Author B. (Type an integer or decimal rounded to four decimal places as needed.

Explanation / Answer

a) p [2 from A and 5 from C] = 9c2 * 8c5 / 22c7 = 36 * 56 / 170544 = 0.0118

b) p[4 from B] = 5c4 * 17c3 / 22c7 = 5*680 / 170544 = 0.0199

c) p [3 from A, 3 from B 1 from C] = 9c3 * 5c3 *8c1 / 22c7 = 84*10*8 / 170544 = 0.0394

d) p [Atleast 5 from A] = 9c5 * 13c2 + 9c6 * 13c1 + 9c7 / 22c7 = 126*78 + 84*13 + 36 / 170544 = 0.0642

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