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∪Flag)/Pr(Flag). The probability that a transaction is flagged is
.001% * 90% + 99.999% * 0.0001% = .000999%.
The Pr(Fraud∪Flag) = .001% * 90% = .0009.
Combining these values,
.0009 /.000999 = 90%.
This indicates that 10% of the flagged transactions are not actually fraudulent.
请问这题的答案解析是不是写错了，按照贝叶斯公式变形后，fraud和flag在分子应该为交集而不是并集吧？
