請教一個機率問題 - 金融分析師

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

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