Re: [問題] 請教一題統計的問題：
先定事件:
會倒債:D 良好評價:F
c c
不會倒債:D 不良的評價:F
※ 引述《jeffho (yeungwailei)》之銘言：
: A customer has approached a bank for a loan. From the past experience, the
: bank believes there is a 10% chance that the customer will default on the
可知P(D)=0.1
: loan. The bank can run a credit check on the customer. The credit check will
: yield either a favorable or an unfavorable report. Historical information
: shows that for those default customers, favorable reports were received 1 out
: of 50 of the time. On the other hand, for those customers that were not default,
P(F|D)=0.02
: favorable reports were received 95 out of 100 of the time. If a favorable report
c
且P(F|D )=0.95
: is received, what is the probability (to 4 decimal places) that the customer
: will default on the loan?
: {Hint: Construct a contingent table of the above problem first.}
: 小弟粗略翻譯了一下中文意思大概是這樣：
: 一個顧客去問銀行借錢，根據過去經驗，銀行認為這傢伙有10%機會不還錢。
: 銀行可以給這人客做一個信用評估，然後這個評估會產生一個好的或是一個不好的報告，
: 以過去的數據統計出，對於那些會逃債的人客。他們每50個報告只有1個是好的報告，
: 而不會逃債的，是每100個報告有95個都是好的，現在我們對這位客人做信用評估，
: 那麼請問如果他得出一個好的報告，他結果會逃債的機率是多少？
所求為P(D|F)
先劃出樹狀圖:
c
F ---D 因為P(D) = 0.1 => P(D ) = 0.9
\
\ c 又 P(F|D) = 0.02 = P(F交D)/P(D) => P(F交D) = 0.002
D
c c c c
且 P(F|D ) = 0.95 = P(F交D )/P(D ) => P(F交D ) = 0.855
c c
F ---D 所以P(F) = P(F交D) + P(F交D ) = 0.857
\
\ c
D 而所求P(D|F) = P(D交F) / P(F) = 0.002/0.857 = 0.0023
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