### Find combinational probability of drawing one color of objects from three different colors by grouping two colors into one large group

Question Sample Titled 'Find combinational probability of drawing one color of objects from three different colors by grouping two colors into one large group'

A box contains ${8}$ red balls , ${4}$ green balls and ${8}$ yellow balls. If ${4}$ balls are randomly drawn from the box at the same time,

 (a) find the probability that exactly ${2}$ red balls are drawn; (2 marks) (b) find the probability that at least ${2}$ red balls are drawn. (2 marks)

 (a) ${P}{\left(\text{exactly two red balls are drawn}\right)}$ $=\dfrac{{{{C}_{{2}}^{{8}}}{{C}_{{2}}^{{12}}}}}{{{{C}_{{4}}^{{20}}}}}$ 1M for numerator $=\dfrac{{616}}{{1615}}$ 1A r.t. ${0.381}$ (b) ${P}{\left(\text{at least two red balls are drawn}\right)}$ $={P}{\left(\text{two red balls}\right)}+{P}{\left(\text{three red balls}\right)}+{P}{\left(\text{four red balls}\right)}$ $=\dfrac{{616}}{{1615}}+\dfrac{{{{C}_{{3}}^{{8}}}{{C}_{{1}}^{{12}}}}}{{{{C}_{{4}}^{{20}}}}}+\dfrac{{{{C}_{{4}}^{{8}}}}}{{{{C}_{{4}}^{{20}}}}}$ 1M for ${\left({a}\right)}+{p}_{{1}}+{p}_{{2}}$ $=\dfrac{{518}}{{969}}$ 1A r.t. ${0.535}$

 (a) ${P}{\left(\text{exactly two red balls are drawn}\right)}$ $={6}{\left(\dfrac{{8}}{{20}}\right)}{\left(\dfrac{{7}}{{19}}\right)}{\left(\dfrac{{12}}{{18}}\right)}{\left(\dfrac{{11}}{{17}}\right)}$ 1M for ${6}$ ${p}_{{3}}{p}_{{4}}{p}_{{5}}{p}_{{6}}$ $=\dfrac{{616}}{{1615}}$ 1A r.t. ${0.381}$   (b) ${P}{\left(\text{at least two red balls are drawn}\right)}$ $={P}{\left(\text{two red balls}\right)}+{P}{\left(\text{three red balls}\right)}+{P}{\left(\text{four red balls}\right)}$ $=\dfrac{{616}}{{1615}}+{4}{\left(\dfrac{{8}}{{20}}\right)}{\left(\dfrac{{7}}{{19}}\right)}{\left(\dfrac{{6}}{{18}}\right)}{\left(\dfrac{{12}}{{17}}\right)}+{\left(\dfrac{{8}}{{20}}\right)}{\left(\dfrac{{7}}{{19}}\right)}{\left(\dfrac{{6}}{{18}}\right)}{\left(\dfrac{{5}}{{17}}\right)}$ 1M for (a)$+{p}_{{7}}+{p}_{{8}}$ $=\dfrac{{518}}{{969}}$ 1A r.t. ${0.535}$   or (b) ${P}{\left(\text{at least two red balls are drawn}\right)}$ $={1}-{P}{\left(\text{no red balls}\right)}-{P}{\left(\text{one red balls}\right)}$ $={1}-\dfrac{{{{C}_{{4}}^{{12}}}}}{{{{C}_{{4}}^{{20}}}}}-\dfrac{{{{C}_{{1}}^{{8}}}{{C}_{{3}}^{{12}}}}}{{{{C}_{{4}}^{{20}}}}}$ 1M for ${1}-{p}_{{9}}-{p}_{{10}}$ $=\dfrac{{518}}{{969}}$ 1A r.t. ${0.535}$

# 專業備試計劃

Level 4+ 保證及 5** 獎賞

ePractice 會以電郵、Whatsapp 及電話提醒練習

ePractice 會定期提供溫習建議

Level 5** 獎勵：會員如在 DSE 取得數學 Level 5** ，將獲贈一套飛往英國、美國或者加拿大的來回機票，唯會員須在最少 180 日內每天在平台上答對 3 題 MCQ。

Level 4 以下賠償：會員如在 DSE 未能達到數學 Level 4 ，我們將會全額退回所有會費，唯會員須在最少 180 日內每天在平台上答對 3 題 MCQ。

# FAQ

ePractice 是甚麼？

ePractice 是一個專為中四至中六而設的網站應用程式，旨為協助學生高效地預備 DSE 數學（必修部分）考試。由於 ePractice 是網站應用程式，因此無論使用任何裝置、平台，都可以在瀏覽器開啟使用。更多詳情請到簡介頁面。

ePractice 可以取代傳統補習嗎？

1. 會員服務期少於兩個月；或
2. 交易額少於 HK\$100。

Initiating...

HKDSE 數學試題練習平台