請教一個機率問題 - 金融分析師

※ 引述《linki (111111)》之銘言：
: 這是actex study manual module 3 poisson process的example 3.20
: 根據3.19的題意延伸
: p(wating time of the claim from Texas
: < wating time of the claim from Missouri)=0.6
: 也就是claim from Texas會比Missouri早發生的機率為0.6
: 而3.20問到
: For the insurance company in the preceding example:
: (a) Find the probablity that three claims from Texas are received before the
: first claim from Missouri.
: (b) Find the probablity that three claims from Texas are received before the
: third claim from Missouri.
: (a)是比較沒問題，就是發生的前三件事都是from Texas
: 所以答案是0.6x0.6x0.6=0.216
: (b)我解讀題意是在第三次的案件來自Missouri前，發生三次案件來自Texas
: 不知道有沒有解讀錯(不好意思，小弟英文不是很好)
: 我的想法是用負二項分配來解題，也就是把claim from Missouri當成功(p=0.4)
: 也就是利用負二項分配計算在第三次成功前，有三次失敗的機率
: c5取3x0.4^3x0.6^3=0.13824
: 但解答出來卻不是如此
: 想請教各位大大是我對題目解讀錯誤
: 還是觀念錯了
: 謝謝各位
: 附上(b)之解答
: Consider the first five claims received. Three claims from Texas will be
: received before the third claim from Missouri if and only if three or more
: of the first five claims come from Texas. The number of claims from Texas in
: the first five claims received follows a binomial distribution with n=5 and
: p=0.6
: The probability that three or more of the first 5claims came from Texas is
: p(3)+p(4)+p(5)=0.6826



假設O是from Texas X是from Missouri
(OOOXX)X
p(3)=C5取3*(.6)^3*(.4)^2=0.3456
(OOOOX)XX
p(4)=C5取4*(.6)^4*(.4) =0.2592
(OOOOO)XXX
p(5)=C5取5*(.6)^5 =0.0777
---------------------------------------------
0.6825

他解答應該是這個意思吧
不過我看不懂題目為何這樣@@

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