问题
单项选择题
Alan Mulally, CFA, is a securities analyst covering IT industry. Mulally finds that 10% of companies he follows filed for bankruptcy. Mulally then conducts a bankruptcy scoring test on all companies and finds that:
·70% of companies passed the test, and
·75% of companies passed the test, given they did not file for bankruptcy.
Using Bayes' formula, given it passed the test, the probability a company filed for bankruptcy is closest to:（）
A. 3.33%
B. 3.57%
C. 8.33%
答案
参考答案：B
解析：
根据题意，已知：70%的企业通过了测试，申报破产的企业比例是10%，则没有申报破产的企业比例是1-10%=90%，在没有申报破产的企业中通过测试的比例是75%。因此，我们要求在申报破产的企业中通过测试的比例，根据全概率公式可得：(70%-75%×90%)/(10%)=25%。
再根据Bayes公式，可得：(25%×10%)/(70%)=3.57%。