# Quod Erat Demonstrandum

## 2015/02/21

### 表面面積

Filed under: Fun,Junior Form Mathematics — johnmayhk @ 7:47 下午
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(more…)

## 2015/02/20

### 鈄截柱體體積

Filed under: Junior Form Mathematics,NSS,Physics — johnmayhk @ 8:25 下午
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1.緣起

$V=A\frac{h_1+h_2+h_3}{3}$

$V=A\frac{0+0+h}{3}=\frac{1}{3}Ah$ (more…)

## 2015/02/17

### 數算球入盒

Filed under: mathematics,NSS,Pure Mathematics — johnmayhk @ 11:40 上午
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（一） (more…)

## 2015/02/03

### 玩 nCr

Filed under: Fun,NSS — johnmayhk @ 3:30 下午
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$C^{m+n}_2=C^m_2+C^n_2+mn$

$C^n_r=\frac{n!}{r!(n-r)!}$

## 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)
=$\frac{2}{5}\frac{1}{4}+\frac{3}{5}\frac{3}{4}\frac{2}{3}+\frac{3}{5}\frac{2}{4}\frac{2}{3}\frac{1}{2}+\frac{3}{5}\frac{2}{4}\frac{1}{3}$
=$\frac{2}{5}$

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