1.A specialist predics that the probabilities that Hang Sang Index will increase to 20300 and 20400 on a day are 0.4 and 0.15 respectively. Given that Hang Sang Index has increased to 20300 on that day, find the probability that Hang Sang Index will increase to 20400 on that day .
(answer:0.375)
2.All letters are taken from the word ‘study’ and then arranged. If ‘U’ and ‘Y’
are not next to each other ,and the first letter is neither ‘U’ nor ‘Y’, how many permtations are there?
(answer:36)
3.A and B have to type an article of 2400 words in a contest. The number of words that A types in a minute is 4 more than the number of words that B types in a minute. And it takes 2.5 minutes longer for B to finish. Find the number of words that B types in a minute.
(answer:60)
我想要步驟 唔該
數學問題 40分
2010-12-18 6:15 am
回答 (2)
2010-12-18 6:37 am
✔ 最佳答案
1 By conditional probability, the probability that Hang Sang Index will increase to 20400 on that day=P(increase to 20300 and 20400)/P(increase to 20300)
=0.15/0.4
=15/40
=0.3752 If U, Y are at the second and forth place, then the no. of permutations is 3!2!=12If U, Y are at the third and fifth place, then the no. of permutations is 3!2!=12If U, Y are at the second and fifth place, then the no. of permutations is 3!2!=12So, there are total 12+12+12=36 permutations.3 Let the number of words that B types in a minute is x. Then the number of words that A types in a minute is x+4So, 2400/(x+4)=2400/x - 2.52400[1/(x+4) - 1/x]=-2.5
-4/[x(x+4)]=-25/24000=-1/960
1/[x(x+4)]=1/3840
x=60 or x=-64 (rejected)So, he number of words that B types in a minute is 60.
2010-12-18 6:57 am
1, 0.15/0.4=0.375
2, 3P1 x (4!-3!x2!)= 3 x 12 = 36
3, let the no. of words B types to be x
and the no. of words A types to be x+4
( 2400/(4+x) ) + 2.5 = 2400/x
2400x + 10x + 2.5(x^2) = 9600 + 2400x
2.5(x^2) + 10x - 9600 = 0
x= 60 or x = -64 (rejeated)
2, 3P1 x (4!-3!x2!)= 3 x 12 = 36
3, let the no. of words B types to be x
and the no. of words A types to be x+4
( 2400/(4+x) ) + 2.5 = 2400/x
2400x + 10x + 2.5(x^2) = 9600 + 2400x
2.5(x^2) + 10x - 9600 = 0
x= 60 or x = -64 (rejeated)
參考: myself
收錄日期: 2021-04-26 14:02:57
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