1.There are 40 students in F.4A. All of them study Computer Studies or Economics or both. It is known that 24 students study Computer Studies and 20 students study Economics.
(a) Find the number of students who study both subjects. [Ans. 4]
(b) If a student is selected at random from the class, find the probability that this student studies only one of the two subjects. [Ans. 9/10 ]
(c) If a student is selected at random from those who study Computer Studies, find the probability that this student also studies Economics. [Ans. 1/6 ]
(d) If 3 students are selected at random from the class, find the probability that at least one of them studies both subjects.[Ans. 137/494 ]
Could anyone show the calculation process in details? thx!
probability problem
2010-04-06 7:17 am
回答 (2)
2010-04-06 7:36 am
✔ 最佳答案
a)(24 + 20) - 40 = 4b)P(this student studies only one of the two subjects)
= 1 - P( this student studies both subjects)
= 1 - 4/40
= 1/9
c) If a student is selected at random from those who study Computer Studies
: 24 student are possible , only 4 studies both ,
So P(E) = 4/24 = 1/6
d) P(at least one of them studies both subjects)
= 1 - P(All 3 selected students are study one subject)
= 1 - (36/40)(35/39)(34/38)
= 1 - (9/10)(35/39)(17/19)
= 1 - (9*35*17) / (10*39*19)
= 1 - (3*7*17) / (2*13*19)
= 1 - 357/494
= 137/494
2010-04-12 13:14:04 補充：
Thankyou eicachan.
2010-04-12 9:08 pm
b)P(this student studies only one of the two subjects)
= 1 - P( this student studies both subjects)
= 1 - 4/40
= 1-1/10
=9/10
= 1 - P( this student studies both subjects)
= 1 - 4/40
= 1-1/10
=9/10
收錄日期: 2021-04-21 22:09:30
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100405000051KK01811