Example 3 (2004 National College Entrance Examination Hubei Paper) A certain emergency event, if no preventive measures are taken, has a probability of 0.3 of occurring; if it occurs, it will cause a loss of 4 million yuan. There are two independent preventive measures, A and B, available for adoption. The costs of adopting preventive measures A and B alone are 450,000 yuan and 300,000 yuan, respectively, and the probabilities of the emergency event not occurring after adopting the corresponding preventive measures are 0.9 and 0.85, respectively. If the preventive plan allows for the adoption of preventive measures A and B alone, in combination, or not at all, please determine the preventive plan that minimizes the total cost.
(Total cost $=$ cost of adopting preventive measures + expected value of losses from the emergency event occurring.)
Analysis This question tests the basic knowledge of probability and the concept of mathematical expectation, as well as the ability to apply probability knowledge to solve practical problems.
Solution (1) Without taking preventive measures, the total cost, which is the expected loss, is $400 \times 0.3=120$ (ten thousand yuan);
(2) If only measure A is taken, the cost of preventive measures is 45 ten thousand yuan, and the probability of a sudden event occurring is $1-0.9=0.1$, the expected loss is $400 \times 0.1=40$ (ten thousand yuan), so the total cost is $45+40=85$ (ten thousand yuan);
(3) If only preventive measure B is taken, the cost of preventive measures is 30 ten thousand yuan, and the probability of a sudden event occurring is $1-0.85=0.15$, the expected loss is $400 \times 0.15=60$ (ten thousand yuan), so the total cost is $30+60=90$ (ten thousand yuan);
(4) If both preventive measures A and B are taken, the cost of preventive measures is $45+30=75$ (ten thousand yuan), and the probability of a sudden event occurring is $(1-0.9)(1-0.85)=0.015$, the expected loss is $400 \times 0.015=6$ (ten thousand yuan), so the total cost is $75+6=81$ (ten thousand yuan).

In summary, comparing the total costs in (1), (2), (3), and (4), it is clear that both preventive measures A and B should be taken to minimize the total cost.
!Comment This question mainly tests the concept of mathematical expectation and knowledge related to independent events.