probability

2007-10-14 9:16 pm
of the 400 pupils in a school,
70 have read magazines A,B and C
100 have read both magazines A and B
80 have read both magazines A and C
90 have read both magazines B and C
150 have read magazines A
170 have read magazines B
160 have read magazines C
(a)(i) how many pupils have read at least one of the magazines?


更新1:

of the 400 pupils in a school, 70 have read magazines A,B and C 100 have read both magazines A and B 80 have read both magazines A and C 90 have read both magazines B and C 150 have read magazines A 170 have read magazines B 160 have read magazines C

更新2:

(a)(ii) how many pupils have read exactly two of the magazines? (a)(iii) how many pupils have read exactly one of the magazines?

更新3:

(b) if one of these 400 pupils is chosen at random, what is the probability that he has not read any of the 3 magazines?

回答 (3)

2007-10-14 9:35 pm
✔ 最佳答案
ai) P( pupils have read at least one of the magazines)
= P(A) + P (B) + P(C) - P(AB) - P(BC)-P(AC) +P(ABC)
= [150+160+170 - (80+90+100) +70]/400
=0.7
pupils have read at least one of the magazines
= 0.7 *400
=280

aii) P( pupils have read at least one of the magazines)
= P(AB) + P(BC)+P(AC) -P(ABC)
= [(80+90+100) -70]/400
= 0.5

pupils have read at least one of the magazines
= 0.5*400
=200

aiii) P(pupils have read exactly one of the magazines)
= P( pupils have read at least one of the magazines) - P( pupils have read at least one of the magazines) - P( pupils have read all three magazines)
= 0.7 -0.5 - 70/400
= 0.025

pupils have read exactly one of the magazines
= 0.025*400
=10

b) P(the pupil has not read any of the 3 magazines)
= 1- P( pupils have read at least one of the magazines)
=1-0.7
=0.3
2007-10-14 9:25 pm
1
17/41
24/41
2007-10-14 9:22 pm
a(1) 1
a(2) 17/41
a(3) 24/41


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