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云烟2023 · 2020年08月19日

问一道题:NO.PZ2020010301000009

问题如下:

Credit card companies rapidly assess transactions for fraud. In each day, a large card issuer assesses 10,000,000 transactions. Of these, 0.001% are fraudulent. If their algorithm identifies 90% of all fraudulent transactions but also 0.0001% of legitimate transactions, what is the probability that a transaction is fraudulent if it has been flagged?

选项:

A.

90%

B.

80%

C.

95%

D.

10%

解释:

We are interested in Pr(Fraud|Flag). This value is Pr(Fraud\capFlag)/Pr(Flag). The probability that a transaction is flagged is

.001% * 90% + 99.999% * 0.0001% = .000999%.

The Pr(Fraud\capFlag) = .001% * 90% = .0009.

Combining these values,

.0009 /.000999 = 90%.

This indicates that 10% of the flagged transactions are not actually fraudulent.

请问这个数学运算怎么做的?我总是算不对

1 个答案

品职答疑小助手雍 · 2020年08月19日

嗨,爱思考的PZer你好:


按数字数也不是不行,这10million的交易里,F的占100个,那L的就是9999900个。

算法标记的数量就是90%*100+9999900*0.0001%=90+9.9999=99.9999个。

现在一笔交易被标记了,那他是F的可能就是90/99.9999=90%


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