This is an exercise designed to reveal some facts of reasoning and decision making. The “fraud involvement procedure” is fictional.

A team of accountants and psychologists has developed a procedure to test for management involvement in fraudulent activities. The procedure consists of developing a personality profile of key managers and comparing each profile with a master profile of a number of individuals who have perpetrated material frauds. If the manager’s profile is sufficiently similar to the master profile, the procedure signals “fraud.” In the last 18 months, the procedure has been tested extensively in the field by a national public accounting firm and has found the following:

• If a key manager has been involved in a material fraud, the procedure indicates “fraud” 8 times out of 10.

• If a key manager has not been involved in a material fraud, the procedure will nonetheless indicate “fraud” 20 times out of 100.

• The evidence indicates that about 10 key managers in 100 have been involved in material fraud.

Required:

Based on these results, what is your assessment of the probability that a key manager who receives a “fraud” test signal is actually involved in fraudulent activities?