GMAT数学 GMAT数学之概率大成篇

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[GMAT数学]GMAT数学之概率大成篇---想的到的简单，想不到的难！

GMAT数学10个基本概念

1、mode（众数）

一堆数中出现频率最高的一个或几个数，例如：mode of 1,1,1,2,3,0,0,0,5 is 1 and0.

2、range（值域）

一堆数中最大和最小数之差，例如：range of 1,1,2,3,5 is 5-1=4 3、mean（平均数）

arithmatic mean（算术平均数），geometric mean （几何平均数：n个数之积的n次方根）

4、median（中数）

将一堆数排序之后，正中间的一个数（奇数个数字），或者中间两个数的平均数（偶数个数字），

例如：“medianof 1,7,4,9,2,2,2,2,2,5,8 is 2”，“median of 1,7,4,9,2,5is (5 7)/2=6”。

5、standard error（标准偏差）

一堆数中，每个数与平均数的差的绝对值之和，除以这堆数的个数(n)。 例如：standard error of 0,2,5,7,6 is: (|0-4| |2-4| |5-4| |7-4| |6-4|)/5=2.4

6、standard variation

一堆数中，每个数与平均数之差的平方之和，再除以n，例如：standardvariation of 0,2,5,7,6 is6.8 7、standard deviation

就是standard variation的平方根.

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标准方差的公式：d^2=[(a1-a)^2 (a2-a)^2 .... (an-a)^2 ]/n，d 为标准方差。

8. 三角形余玄定理

C^2=A^2 B^2-2ABCOSt，其中t为AB两条线间的夹角。 9. Y=k1X B1,Y=k2XB2，两线垂直的条件为K1K2=-1

10. 三的倍数的特点：所有位数之和可被3整除。

概率题

GMAT数学概率题是最容易掌握的一类GMAT数学题型，解决这类题，用两种主要的方法就可以解决，就是加法原则和乘法原则：问自己这个事儿完成了没有?如果完成了就是加法原则，没有完成就是乘法原则。

例子一：从北京到上海可以乘飞机(3种方案)，轮船(2种方案)，或者火车(5种方案)，问从北京到上海乘这3种交通工具共几种方案?答：既然任何一个方案都已经到达了上海，这件事儿已经完成了，所以用加法原则：3+2+5=10种

例子二：从北京到上海有2条路线，从上海到深圳有5条路线，问从北京出发经由上海到深圳会有多少种路线?答：当你到达上海时还没有到达深圳呢，没有完成，那就乘起来，用乘法原则： 2×5=10

题目大讨论

求一道概率题

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大家来看看这倒概率题

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请教一道头疼的概率题

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概率题，求解

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你的show time（欢迎大家来帖讨论呦！）

1. In how many ways can 9 people be seated in a row of chairs if two of the people, David and Becky, refuse to sit together?

2. A fair coin is tossed 10 times. What is the probability that two heads do not occur consecutively?

3. Cain prepared 4 different letters to be sent to 4 different addresses. For each letter, he prepared an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, 1) what is the probability that only 1 letter will be put into the envelop with its correct dress? 2)that no letter will be put into the envelope with its correct address? 3)that all letters will be put into the envelope with its correct ad dress?

4. There are y different travelers who each have a choice of vacationing at one of N different destinations. What is the probability that all y travelers will end up vacationing at the same destination?

5. A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

6. A certain basket contains 10 apples, 3 of which are green and 7 of

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them are red. If three different apples are selected at random from the basket, what is the probability that 2 of them are red and 1 of them is green?

7. A certain telephone number has seven digits. If the telephone number has the digit zero exactly 3 times, and the number 1 is not used at all, what is the probability that the phone number contains one or more prime digits.

8. Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 three-person sub committees, what percent of all the possible subcommittees that include Michael also include Anthony?

9. Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sits together in adjacent chairs?

10. A committee of three people is chosen from five married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?

11. From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the

probability that equal numbers of boys and girls will be selected?

12. A box contains 10 pairs of shoes (20 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?

13. Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny $1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability that Kate has more than $10 but less than $15?

14. A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?

15. A fair coin with sides marked heads and tails is to be tossed eight

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