a*****g
发帖数: 1320 | 1 【 以下文字转载自 SanFrancisco 讨论区 】
发信人: ashuang (不要迷恋哥，哥只是个传说), 信区: SanFrancisco
标 题: mathscounts 数学题求助
发信站: BBS 未名空间站 (Fri Oct 29 00:35:22 2010, 美东)
1.WHAT IS THE PROBABILITY THAT A RANDOMLY SELECTED TWO -DIGIT POSITIVE
INTEGER IS A PERFECT SQUARE OR A PERFECT CUBE? EXPRESS YOUR ANSWER AS A
COMMON FRACTION.
2. A FIVE DIGIT NUMBER IS CREATED USING THE DIGITS 1-5 EACH ONCE.WHAT IS THE
PROBABILITY THAT THE NUMBER IS ODD? EXPRESS YOUR ANSWER AS A COMMON
FRACTION.
3.THE DIGITS 2,3, 4, 7 AND 8 ARE EACH USED ONCE TO FORM A FIVE DIGIT NUMBER
. WHAT IS THE PROBABILITY THAT THE TENS DIGIT IS ODD AND THE NUMBER IS
DIVISIBLE BY 4? EXPRESS YOUR ANSWER AS A COMMON FRACTION
4.THE SUM OF THE DIGITS OF A NUMBER IS 9.WHAT IS THE PROBABILITY THAT THE
NUMBER IS PRIME?
本人无力辅导儿子的数学竞赛，请好心人给出解题步骤，衷心感谢了。 | p******r
发帖数: 2999 | 2 1. square: 1, 4, 9, 16, 25, 36, 49, 64, 81
cube: 1, 8, 27, 64
prob=12/99=4/33
2. the last digit determines parity. to make it odd, it must be 1,3,5
prob=3/5
3. if the number is multiple of 4, then the last two digits must be
divisable by 4. given the tens digit is odd, it can be 32, 72
prob=2/(5*4)=1/10
4. zero. because it can be divided by 3.
THE
NUMBER
【在 a*****g 的大作中提到】
: 【 以下文字转载自 SanFrancisco 讨论区 】
: 发信人: ashuang (不要迷恋哥，哥只是个传说), 信区: SanFrancisco
: 标 题: mathscounts 数学题求助
: 发信站: BBS 未名空间站 (Fri Oct 29 00:35:22 2010, 美东)
: 1.WHAT IS THE PROBABILITY THAT A RANDOMLY SELECTED TWO -DIGIT POSITIVE
: INTEGER IS A PERFECT SQUARE OR A PERFECT CUBE? EXPRESS YOUR ANSWER AS A
: COMMON FRACTION.
: 2. A FIVE DIGIT NUMBER IS CREATED USING THE DIGITS 1-5 EACH ONCE.WHAT IS THE
: PROBABILITY THAT THE NUMBER IS ODD? EXPRESS YOUR ANSWER AS A COMMON
: FRACTION.
| a*****g
发帖数: 1320 | 3 谢谢你。
【在 p******r 的大作中提到】
: 1. square: 1, 4, 9, 16, 25, 36, 49, 64, 81
: cube: 1, 8, 27, 64
: prob=12/99=4/33
: 2. the last digit determines parity. to make it odd, it must be 1,3,5
: prob=3/5
: 3. if the number is multiple of 4, then the last two digits must be
: divisable by 4. given the tens digit is odd, it can be 32, 72
: prob=2/(5*4)=1/10
: 4. zero. because it can be divided by 3.
:
| s*****n
发帖数: 742 | 4 抛砖引玉哈
1. from 10 to 99, you have 16, 25 ... 81 and 27, 64 = 8
then the answer is 8/90 = 4/45
2. 1-5
say the last digit is 1, then u have P(4*4) for the first 4 digits.
then the answer will be 3 * P(4*4) / 5 * P(4*4) = 3/5 | a*****g
发帖数: 1320 | 5 也谢谢你。
【在 s*****n 的大作中提到】
: 抛砖引玉哈
: 1. from 10 to 99, you have 16, 25 ... 81 and 27, 64 = 8
: then the answer is 8/90 = 4/45
: 2. 1-5
: say the last digit is 1, then u have P(4*4) for the first 4 digits.
: then the answer will be 3 * P(4*4) / 5 * P(4*4) = 3/5
| p******r
发帖数: 2999 | 6 just realized 1 isn't a two digit number :)
i was thinking 01, 02, and etc
prob=7/90
【在 p******r 的大作中提到】
: 1. square: 1, 4, 9, 16, 25, 36, 49, 64, 81
: cube: 1, 8, 27, 64
: prob=12/99=4/33
: 2. the last digit determines parity. to make it odd, it must be 1,3,5
: prob=3/5
: 3. if the number is multiple of 4, then the last two digits must be
: divisable by 4. given the tens digit is odd, it can be 32, 72
: prob=2/(5*4)=1/10
: 4. zero. because it can be divided by 3.
:
| a*****g
发帖数: 1320 | 7 谢谢！ 可不可以解释下第三题？
【在 p******r 的大作中提到】
: just realized 1 isn't a two digit number :)
: i was thinking 01, 02, and etc
: prob=7/90
| p******r
发帖数: 2999 | 8 能被4整除，意味着最后两位能被4整除
所以只能是32,72
而最后两位排列组合有10种情况
所以概率为1/5
【在 a*****g 的大作中提到】
: 谢谢！ 可不可以解释下第三题？
| a*****g
发帖数: 1320 | 9 １／１０？
【在 p******r 的大作中提到】
: 能被4整除，意味着最后两位能被4整除
: 所以只能是32,72
: 而最后两位排列组合有10种情况
: 所以概率为1/5
| p******r
发帖数: 2999 | 10 2/10...
【在 a*****g 的大作中提到】
: １／１０？
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