二树杈法

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$\cap$Flag)/Pr(Flag). The probability that a transaction is flagged is

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

The Pr(Fraud$\cap$Flag) = .001% * 90% = .0009.

Combining these values,

.0009 /.000999 = 90%.

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