## Boolean financial advisors

Alex and Bob work as financial advisors for the same company. They draw equal salaries from the company. They behave well at the office. Both work on similar assignments. Each assignment requires a yes-no decision. The company uses the decisions made by them to make profits.

After the recession hit the company very badly, one of them has to be fired. Both Alex and Bob have worked on almost the same number of assignments in the last ten years. Alex has been consistently taking about 80% decisions correctly every year. Bob, on the other hand, has been taking only about 5% correct decisions every year.

Assuming that the performances of Alex and Bob would remain the same in future, who should the company fire to maximize its profits in the years to come? Why?

[SOLVED]

### 5 comments

#### Abhishek Sethi solved this puzzle:

Alex should be fired. Since a yes-no decision has to be taken, Bob being 5% right is equivalent to Bob being 95% wrong. If every decision of Bob is inverted, we get 95% accuracy.

#### Rino Raj solved this puzzle:

Consistently 95% wrong means the company could reverse each decision and be 95% right. Hence Bob should be retained. Alex should be fired.

#### Indhu Bharathi solved this puzzle:

Fire Alex and inverse Bob's decisions to get a success rate of 95%.

#### Gnanasenthil G solved this puzzle:

Alex should be fired. Bob takes only 5% correct decisions. The company can do the exact opposite of what Bob recommends and take 95% right decisions. However, Alex can help the company take only 80% right decisions.

#### Reiner Rückwald solved this puzzle:

If Bob keeps on performing so badly that 95% of his decisions are taken wrongly every year, then the company should better keep him and fire Alex instead, provided that the company always inverts Bobs decisions and decides upon the opposite. This ensures that 95% of those decisions are taken correctly to maximize the company's profit.
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