# Quod Erat Demonstrandum

## 2018/04/17

### 互斥與獨立

Filed under: NSS — johnmayhk @ 12:37 下午
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## 2015/02/01

### 黑白球

Filed under: mathematics,NSS — johnmayhk @ 10:33 上午
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In a game, Evan has to draw balls from a bag containing 2 black balls and 3 white balls one by one without replacement. If he gets two consecutive black balls, he wins; otherwise he loses. Find the probability that he wins.

P(wins)
=P(BB)+P(WBB)+P(WWBB)+P(WWWBB)
=$\frac{2}{5}\frac{1}{4}+\frac{3}{5}\frac{3}{4}\frac{2}{3}+\frac{3}{5}\frac{2}{4}\frac{2}{3}\frac{1}{2}+\frac{3}{5}\frac{2}{4}\frac{1}{3}$
=$\frac{2}{5}$

$\frac{3}{7}\frac{2}{6}+\frac{4}{7}\frac{3}{6}\frac{2}{5}+\frac{4}{7}\frac{3}{6}\frac{3}{5}\frac{2}{4}+\frac{4}{7}\frac{3}{6}\frac{2}{5}\frac{3}{4}\frac{2}{3}+\frac{4}{7}\frac{3}{6}\frac{2}{5}\frac{1}{4}=\frac{3}{7}$

## 2015/01/23

### 某數算題

Filed under: mathematics,NSS — johnmayhk @ 5:34 下午
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Just reply to a F.5C student on a basic core mathematics question (on P.5.38):

There are 8 outstanding students from junior forms and 9 outstanding students from senior forms in a school this year. 5 out of these 17 students are now selected for an overseas exchange programme. Find the number of combinations of selecting at least 1 student from junior forms and 1 from senior forms.

Here is the ‘so-called’ solution from a student:

$_8C_1\times _9C_1\times _{15}C_3$

as the student claimed, select 1 from junior, $_8C_1$ ways; select 1 from senior, $_9C_1$ ways; then select the remaining 3 students from the remaining 15 students, $_{15}C_3$ ways, hence, the total number of combination should be $_8C_1\times _9C_1\times _{15}C_3$, right?

Sorry, it is incorrect. (more…)

## 2014/02/21

### 某概率題

Filed under: NSS — johnmayhk @ 3:15 下午
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$\frac{C_2^7}{C_6^{11}}$

## 2014/02/01

### 某數型

Filed under: Fun — johnmayhk @ 5:59 下午
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2,3,4,…,12

## 2014/01/01

### HT

Filed under: Additional / Applied Mathematics,Fun,HKALE — johnmayhk @ 12:27 上午
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(a) THT 比 TTT 先出現；
(b) TTT 比 THT 先出現。

HHTHHHHTHTHHHTT… 就是 (a) 其中一種情況；
HTTHHHTTHHTTTHT… 就是 (b) 其中一種情況；

## 2013/02/07

### To 5E

Filed under: NSS — johnmayhk @ 5:09 下午
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Q.1

(a) John 被抽出玩快活角遊戲之機會；
(b) John 成為快活角遊戲主角之機會。

(more…)

## 2012/02/13

### Core Math 某題：概率

Filed under: NSS,Teaching — johnmayhk @ 11:14 上午
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In a lucky draw of a car, only 1 key out of 10 can open the door of the car. Chris, Rachel and Mike take turns to draw a key at random without replacement. The person who can open the car door will get the car. Find the probabilities of the following events happening.

(a) Chris will get the car.
(b) Rachel will get the car.
(c) Mike will get the car.

## 2010/12/23

### to 5D

Filed under: Additional / Applied Mathematics,NSS — johnmayhk @ 11:32 下午
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Solution to questions (2010-12-22 worksheet)

1.
Toss a fair coin 10 times.

P(exactly 6 “H” and 4 “T”)

## 2010/06/17

### 重複數算一例

Filed under: Additional / Applied Mathematics,HKALE — johnmayhk @ 11:05 上午
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http://www.hkms-nss.net/discuz/home/space.php?uid=423&do=blog&id=38

## 2010/06/01

### Just a revision on counting

Filed under: Additional / Applied Mathematics,HKALE,Teaching — johnmayhk @ 4:03 下午
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Here is just an ordinary question:

“An elevator starts carrying five persons at the ground floor and then goes up. It can stop at any floor of the building (from the first floor to the third floor). Events that people leaving the elevator are assumed to be independent. Let X be the number of ‘stop’ of the elevator during a “going-up” journey. Find the value of E(X)."

We may use “balls and boxes" (more…)

## 2010/05/27

### just answer a textbook question from my student

Filed under: Additional / Applied Mathematics,HKALE — johnmayhk @ 12:45 下午
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To Lau (my student)

This is the question you’d asked

“A man lives at A and works at C, and is due at work at 8:30 a.m. He always catches the first train from A to B, which is scheduled to arrive at B at 8:15 a.m. Buses leaves B for C every 20 minutes, and the bus which leaves B at 8:20 a.m. is scheduled to arrive outside the factory at C at 8:27 a.m. The train is, on the average, one minute late and has a standard deviation of 4 minutes. The bus always leaves on time, but is, on the average, 1.5 minutes late with a standard deviation of 2 minutes. The man’s employer leaves home in his car at 8:15 a.m. and the time for his journey has mean value 13 minutes with a standard deviation of 3 minutes. Find the probability that the employer arrives before the employee." (more…)

## 2010/03/14

### 查表前先查表

Filed under: Additional / Applied Mathematics,Fun,HKALE — johnmayhk @ 6:30 下午
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## 2010/01/08

### 圓桌會意

Filed under: Additional / Applied Mathematics,HKALE,Teaching — johnmayhk @ 4:04 下午
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「16 人，當中包括兩對夫婦，隨意被安排坐有 16 座位的圓桌，求該兩對夫婦並排而坐（sit next to each other）之概率。」