probability

myteapot172000

2011-05-05 3:41 am

A Mathematics examination consists of two papers, paper I and paper II. The results of 200 students in the two papers are as follow:

121 students pass paper I
120 students pass paper II
85 students pass paper I and paper II

A student is chosen at random from the 200 students. What are the properbilities that the student chosen

(a)(i) passed paper I given that he has passed paper II?
(a)(ii) passed paper II given that he has passed paper I?
(a)(iii) passed paper I or paper II?

(b) Two students are chosen at random from the 200 students. What are the properbilities that

(i) the two students chosen has failed both paper I and paper II?
(ii) exactly one of the students has passed paper I given that both has passed paper II?

回答 (1)

myisland8132

2011-05-05 5:20 am

✔ 最佳答案

N(I) = 121, N(II) = 120, N(I and II) = 85

N(I or II) = 121 + 120 - 85 = 156

(a)(i) P(I | II) = 85/120 = 17/24

(ii) P(II | I) = 85/121

(iii) 156/200 = 39/50

(b)(i) C(44,2)/C(200,2) = 0.04753

(ii) 85*35/C(120,2) = 5/12

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