To enter a certain university, a student must sit for an entrance exam first. If hhe passes the exam he will be invited for an interview. he will enter the university if he also pass the interview. The student who fail in the interview must sit for entrance exam again. The passing % of entrance exam and the interview are 60% and 1/3 respectively.
a) find the probability that a student enters the university by sitting the entrance exam only once
b) find the probability that a student enters the university by sitting the entrance exam exactly twice.
c) if a student is not allowed to sit for the entrance exam more than 3 times ,find the probability that he enters the university with one interview only.
please help me to calculate the above question!!!! thank you very much!!!!
maths question probability
2011-10-07 6:24 am
回答 (3)
2011-10-07 9:22 am
✔ 最佳答案
1E,2E, 3E : 1st exam, 2nd exam and 3rd exam respectively1I, 2I, 3I : 1st interview, 2nd interview, and 3rd interview respectively
P : pass
F : fail
=====
a)
P (entersthe university by sitting the entrance exam only once)
= P(1E-P) ´ P(1E-P)
= 60% ´ (1/3)
= 0.2
=====
b)
P(entersthe university by sitting the entrance exam only twice)
= P(F in the 1st attempt) ´ P(P in the 2nd attempt)
= (1 - 0.2) ´ [60%´ (1/3)]
= 0.08 + 0.08
= 0.16
=====
c)
P(entersthe university by sitting the entrance exam only thrice)
= P(F in the 1st and 2nd attempts) ´ P(P in the 3rd attempt)
= [1 - (0.2 + 0.16)] ´ [60% ´ (1/3)]
= 0.128
P(enters the university with one attempt | at most 3 attempts)
= 0.2 / (0.2 + 0.16 + 0.128)
= 0.2/0.488
= 25/61
2011-10-09 10:16:11 補充：
我也想過這問題。但我只當作是出問題者的語言表達不清。若果真的如 doraemonpaul 所說的語言陷阱，只是出題者的問題，不是我理解的問題了。
參考: 土扁
2011-10-07 4:37 pm
土扁，c部你中招了！
c部是問你只遇過1次interview就入到大學的概率，而不是問你在所有入到大學的學生之中抽到只遇過1次interview就入到大學的學生的概率。
由於只遇過1次interview就入到大學的學生只可能是只考1次entrance exam就入到大學的學生，因此c部的結果其實即是等於a部的結果。
緊記出現If這類的字眼並不是使用條件概率之金科玉律，需要視乎情況而定。
c部是問你只遇過1次interview就入到大學的概率，而不是問你在所有入到大學的學生之中抽到只遇過1次interview就入到大學的學生的概率。
由於只遇過1次interview就入到大學的學生只可能是只考1次entrance exam就入到大學的學生，因此c部的結果其實即是等於a部的結果。
緊記出現If這類的字眼並不是使用條件概率之金科玉律，需要視乎情況而定。
2011-10-07 6:38 am
let say there are totally 100 students:
a) 100 x 60% x 1/3 = 20/100(students) = 1/5
b) 100 x 60% x 2/3 = 40/100(students) = 2/5
c) 100 x 60% x 1/3 x1/3 x 1/3 = 20/9
Q c I don't know the Q is exactly right or not
a) 100 x 60% x 1/3 = 20/100(students) = 1/5
b) 100 x 60% x 2/3 = 40/100(students) = 2/5
c) 100 x 60% x 1/3 x1/3 x 1/3 = 20/9
Q c I don't know the Q is exactly right or not
收錄日期: 2021-04-13 18:17:05
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20111006000051KK00954