Of the 400 pupils in a school ,
70 have read magazine A, B and C ,
100 have read both magazine A and B ,
80 have read both magazine A and C ,
90 have read both magazine B and C ,
150 have read magazine A,
170 have read magazine B,
160 have read magazine C.
(a)
(i) How many pupils have read at least one of the magazines?
(ii) How many pupils have read exactly two of the magazines?
(iii) How many pupils have read exactly one of the magazines?
(b)
If one of these 400 pupils is chosen at random , what is the probability that he has not read any of the three magazines?
thanks a lot for all your help~
probability ... ce question (1979)
2008-10-15 4:15 am
回答 (3)
2008-10-15 7:02 am
✔ 最佳答案
我代Copestone答啦只要用set去想就好易
n(A∩ B∩ C)=70
n(A∩ B)=100
n(A∩ C)=80
n( B∩ C)=90
n(A)=150
n(B)=170
n(C)=160
n(A U B U C)=n(A)+n(B)+n(C)-n(A∩ B)-n(A∩ C)-n(B∩ C)+n(A∩ B∩ C)=280
(ii)
Consider how many pupils only read A and B
Number=n(A∩ B)-n(A∩ B∩ C)=30
Similarly, for the other two
The required number=30+20+10=60
(iii)
Using the concept of (ii)
The required number=40+50+60=150
Draw a Venn diagram can help you
(b)
There are 400-280=120 pupils do not read any of the three magazines
The probability that he has not read any of the three magazines
=120/400
=1/3
Actually this type of questions have been out-syllabus
2008-10-15 10:34 pm
n(A∩ B∩ C)=70
n(A∩ B)=100
n(A∩ C)=80
n( B∩ C)=90
n(A)=150
n(B)=170
n(C)=160
n(A U B U C)=n(A) n(B) n(C)-n(A∩ B)-n(A∩ C)-n(B∩ C) n(A∩ B∩ C)=280
(ii)Consider how many pupils only read A and B
Number=n(A∩ B)-n(A∩ B∩ C)=30
Similarly for the other two
The required number=30 20 10=60
(iii)Using the concept of (ii)
The required number=40 50 60=150
Draw a Venn diagram can help you
(b)There are 400-280=120 pupils do not read any of the three magazines
The probability that he has not read any of the three magazines
=120/400
=1/3
n(A∩ B)=100
n(A∩ C)=80
n( B∩ C)=90
n(A)=150
n(B)=170
n(C)=160
n(A U B U C)=n(A) n(B) n(C)-n(A∩ B)-n(A∩ C)-n(B∩ C) n(A∩ B∩ C)=280
(ii)Consider how many pupils only read A and B
Number=n(A∩ B)-n(A∩ B∩ C)=30
Similarly for the other two
The required number=30 20 10=60
(iii)Using the concept of (ii)
The required number=40 50 60=150
Draw a Venn diagram can help you
(b)There are 400-280=120 pupils do not read any of the three magazines
The probability that he has not read any of the three magazines
=120/400
=1/3
參考: my maths knowledge
2008-10-15 3:40 pm
(a)(i) 280
(ii) 60
(iii) 150
(b) 3/10
If no one answers you in detail, then I shall post the details one week later.
(ii) 60
(iii) 150
(b) 3/10
If no one answers you in detail, then I shall post the details one week later.
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