There are four $10 banknotes and x $20 banknotes in Mr. Leung's pocket. It is given that if two banknotes are picked at random, find the probability of picking two $20 banknotes is 1/3.
(a) Prove that x^2 - 5x - 6 = 0.
(b) If two banknotes are picked at random, find the probability that the total value of the banknotes is $30.
*唔該詳解
F.5 math-probability(3)
2011-02-27 8:11 pm
回答 (1)
2011-02-27 8:25 pm
✔ 最佳答案
(a) Total banknotes = x + 4P(picking $20 banknotes) = 1/3
[x/(x + 4)][(x - 1)/(x + 3)] = 1/3
3x(x - 1) = (x + 3)(x + 4)
3x^2 - 3x = x^2 + 7x + 12
x^2 - 5x - 6 = 0
(b) Solve the equation obtained in (a) x = 6
P(Total value of the banknotes is $30)
= P(1st $10, 2nd $20) + P(1st $20, 2nd $10)
= (4/10)(6/9) + (6/10)(4/9)
= 48/90
= 8/15
收錄日期: 2021-04-13 17:51:44
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https://hk.answers.yahoo.com/question/index?qid=20110227000051KK00421