statictics probability (15分)

2008-11-26 4:40 am

1. A company runs a competition advertised in three national daily newspapers A, B and
C, which have large readerships in the proportions 2:3:1 respectively. Each reader
reads one newspaper only. The proportions of the readerships of A, B and C who enter
the competition are 0.02, 0.01 and 0.05 respectively. You may assume that all entries
to the competition are correct, and if drawn would receive a prize. All entries are
equally likely to be drawn.
(i) What are the probabilities that the top prize is won by a reader of paper A, B or C
respectively?
(ii) What is the probability that the top prize and the second prize are both won by
readers of paper A?
(iii) What is the probability that the top prize and the second prize are won by readers
of two different papers?
(iv) What is the probability that the top three prizes are won by readers of all three
different papers?

回答 (1)

用戶246971

2008-11-27 4:40 am

✔ 最佳答案

(i)
A: (2/6 * 0.02) / (2/6*0.02 + 3/6*0.01 + 1/6*0.05) = 1/3
B: (3/6 * 0.01) / (2/6*0.02 + 3/6*0.01 + 1/6*0.05) = 1/4
C: (1/6 * 0.05) / (2/6*0.02 + 3/6*0.01 + 1/6*0.05) = 5/12

(ii)
assume the volume is very large, so the difference in the probability of top prize, second prize and third prize is neglible.

prob. of both top & 2nd prize are reader of A = 1/3 * 1/3 = 1/9

(iii) combinations are AB, AC, BA, BC, CA, CB
prob = 1/3*1/4 + 1/3*5/12 + 1/4*1/3 + 1/4*5/12 + 5/12*1/3 + 5/12*1/4
= 47/72

or you can calculate as
1 - 1/3*1/3 - 1/4*1/4 - 5/12*5/12 = 47/72

(iv) combinations are ABC, ACB, BAC, BCA, CAB, CBA

prob = 6 * 1/3*1/4*5/12
= 5/24

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