✔ 最佳答案
( In the following answers , nCr = (n!)/((r!)((n-r)!)) )
a) Answer is 24C3 = 24!/((3!)(21!)) = 2024 ( 唔用nPr,因為響呢個case,ABC的排序不重要 ( i.e. (A,B,C)=(C,B,A) , 在nPr中 , (A,B,C)=\=(C,B,A) )
b) 有兩種計法
1st Method :
又於population = 24 之中有兩個contaminated , 而sample=3 之中又係兩個contaminated , 所以呢 , 如果要在3個bottles中一定要有兩個contaminated,咁即係:
Let C = Contaminated的bottles , and N represents non-C = 没有contaminated的bottles , so C 有2個,N有22個,由於我地要搵的是(C,C,N) , 兩個C又一定係果2個bottle , 所以(C,C,N) 會有相等於Numbers of bottles of Type N , 即是24-2=22個組合
咁所以 probability = 22/(24C3) = 1/92
2nd method :
其實呢個即係 hypergeometric distribution ( 超幾何分佈 ) (
http://hk.search.yahoo.com/search?p=hypergeometric+distribution&fr=FP-tab-web-t-ac&fr2=tab-web&ei=UTF-8&n=10&meta=rst%3Dhk&tmpl=&myip= )
條式係 : (以下的nCr寫作(n,r))
P(X=x) = (A,x)(N-A,n-x)/(N,n)
where P(X=x) = The probability of x successes , n = sample size , N = population size , A = No. of successes in the population , N-A=No. of failures in the population , X = No. of successes in the sample , n-x = number of failures in the sample , x = Number of successes in the sample
So , From the original question , A=2,x=2,N=24,n=3, so N-A=22 and n-x=1
So the probability = (2,2)(22,1)/(24,3)=1/92
2007-12-16 22:14:17 補充：
Re : 我可以甘做嗎?? b果題 p(the two contaminated bottles are selected for testing)=1-(22/24)(21/23)(20/22) answer : 咁樣做唔啱架喎
2007-12-16 22:20:15 補充：
1-(22/24)(21/23)(20/22) 乃 the probability that at least 1 contaminated bottle ( =1 bottle ) are selected for testing
2007-12-16 22:21:01 補充：
(大過或者等於1 bottle)*
2007-12-16 22:43:26 補充：
(大過或者等於1 contaminated bottle)*
