P SAMPLE NO.43 - 金融分析師

下禮拜要考P...超緊張...
這邊有個SAMPLE中關於negative binominal的問題:
希望有大大幫忙解惑

A company takes out an insurance policy to cover accidents that occur at its
manufacturing plant. The probability that one or more accidents will occur during
any given month is 3/5. The number of accidents that occur in any given month
is independent of the number of accidents that occur in all other months.
Calculate the probability that there will be at least four months in which no accidents
occur before the fourth month in which at least one accident occurs.

解答提供其中一個做法:

4! 5! 6!
(2/5)^4 + -------*[(2/5)^4]*(3/5)+-------*[(2/5)^4]*(3/5)^2+-------*[(2/5)^4]*(3/5)^3=0.2898
3!*1! 3!*2! 3!*3!

which can be derived directly or by regarding the problem as a negative binomial
distribution with
i) success taken as a month with no accidents
ii) k = the number of failures before the fourth success, and
iii) calculating Pr[k>=3]

我不是很懂為什麼要讓2/5每一項都要到四次方
想很久還是想不懂
麻煩大家了 感激不盡...

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