3 men and 7 women are ranked according to their scores on an exam. Assume that no two scores are alike, and that all 10! possible rankings are equally likely. Let X denote the highest ranking achieved by a man (so X=1 indicates that a man achieved the highest score on the exam). Find each of the following: P(X=2)= P(X=6)= P(X=7)=
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7 men and 3 women are ranked according to their scores on an exam. Assume that no two scores are alike, and that all 10! possible rankings are equally likely. Let X denote the highest ranking achieved by a woman (so X=1 indicates that a woman achieved the highest score on the exam). Find each of the following: P(X=1), P(X=3), P(X=5), P(X=10).
Rashmi S.
Five men and 5 women are ranked according to their scores on an examination. Assume that no two scores are alike and all possible rankings are equally likely. Let X denote the highest ranking achieved by a woman(for instance X=1 if the top ranked person is female) Find P(X=i), I=1,2,3,4,,,,8,9,10.
Aria Y.
3. (Chapter 4, Problem 4) Five men and five women are ranked according to their scores on an examination. Assume that no two scores are alike and all 10! possible rankings are equally likely. Let X denote the highest ranking achieved by a woman. (For instance, X = 1 if the top-ranked person is female.) Find P(X = i), i = 1, 2, 3, ..., 8, 9, 10. SOLUTION: X can take on the values 1, 2, 3, 4, 5, and 6. The p.m.f. is p(1) = 5/10 p(2) = (5 * 5) / (10 * 9) p(3) = (5 * 4 * 5) / (10 * 9 * 8) p(4) = (5 * 4 * 3 * 5) / (10 * 9 * 8 * 7) p(5) = (5 * 4 * 3 * 2 * 5) / (10 * 9 * 8 * 7 * 6) p(6) = (5 * 4 * 3 * 2 * 1 * 5) / (10 * 9 * 8 * 7 * 6 * 5) To work out one value more explicitly, say p(3), this is P(X = 3) = P(the highest ranked female is ranked # 3)
David N.
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