问题 问答题

甲、乙、丙三人同时独立地向同一目标射击,各打一发子弹,命中率分别为0.4,0.5和0.6,目标中一、二、三弹而被击毁的概率分别为0.2,0.4和0.8.
(Ⅰ) 求目标被击毁的概率P;
(Ⅱ) 已知目标被击毁,求目标中三弹的概率q.

答案

参考答案:设A表示事件“目标被击毁”,Bi表示事件“目标中i弹”(i=0,1,2,3),由事件的独立性,得
P(B0)=(1-0.4)(1-0.5)(1-0.6)=0.12,
P(B1)=0.4×(1-0.5)(1-0.6)+(1-0.4)×0.5×(1-0.6)+(1-0.4)(1-0.5)×0.6
=0.38,
P(B2)=0.4×0.5×(1-0.6)+0.4×(1-0.5)×0.6+(1-0.4)×0.5×0.6=0.38,
P(B3)=0.4×0.5×0.6=0.12.
事件B0,B1,B2和B3是该随机试验的完备事件组.
(Ⅰ)根据全概率公式,得
[*]
(Ⅱ)根据贝叶斯公式,得
[*]

解析:

[分析]: 目标中一弹有三种情形:甲击中目标而乙和丙未击中;乙击中目标而甲和丙未击中;丙击中目标而甲和乙未击中.目标中二弹也有三种情形,而目标中三弹只有一种情形.没有一弹击中目标也只有一种情形,且此时目标肯定没有被击毁.利用独立性可求得目标中i(i=0,1,2,3)弹的概率,利用全概率公式可求得p,利用贝叶斯公式可求得q.

单项选择题

In Idaho’s Snake River Valley, where potato farmers depend on electric pumps to water their crops, the state’s largest power company hopes to stand tradition on its head and profit by selling farmers less, not more, electricity. To do that, Idaho Power is vastly expanding its energy-efficiency programs for 395,000 residential customers, small businesses, and farmers. Usually the more customers save, the less utilities make. But under an innovative deal with state regulators in March, Idaho Power gets paid for its plants and equipment and boosts profits by winning incentive payments for reducing electric demand.
It’s an idea that appears to be catching on as legislatures fret about global warming and utilities scramble to meet rising demand without the increasing harassment and cost of building new power plants. Idaho is among 13 states whose regulators have either adopted or proposed measures in the past year to decouple utility profit from electricity production. Decoupling is advancing even faster for natural-gas utilities, with 25 states either adopting or proposing decoupling plans in recent years. "This wave toward ’decoupling’ is clearly gathering momentum," says Martin Kushler of the American Council for an Energy-Efficient Economy in Washington. "More states seem to be calling every week to find out about this."
Although California pioneered the idea 25 years ago—and strengthened incentives and penalties last month—interest is picking up again because of global warming, experts say. The main idea is that by rearranging the incentive structure, regulators can give utilities clear incentives to push energy efficiency and conservation without hurting their bottom lines. Under the new rules in California, for example, electric utilities could make as much as $150 million extra if they can persuade Californians to save some $2 billion worth of power, according to the Natural Resources Defense Council.
"This is a vital step in the global-warming fight," says Audrey Chang, an NRDC researcher. "It represents, we hope, a historic shift toward decoupling that is going to help bend the energy demand curve downwards." Beside Idaho, states that this year adopted decoupling for some or all of its electric power industry include New York, Connecticut, and Vermont. At least nine other states have seen major decoupling proposals this year.
Idaho Power is happy that its key fixed costs—plants and equipment—are now separated from variable costs of electricity sales such as fuel. Regulators annually readjust those fixed rates—up or down—a maximum of 3 percent to ensure that the company gets no more or less than it has been regulated to receive. But customers should benefit, too, as utility efficiency programs cut energy use and energy bills—something the company is trying hard to do so it can win a bonus if it meets or exceeds energy—cutting goals. "Before there was almost a disincentive to go hard at efficiency because we weren’t recovering our fixed costs," says Mike Youngblood, an analyst for Idaho Power. "Now the anticipation is that we will recover our fixed cost, no more or less. And our customers will see their bill go down if they invest in energy efficiency."
One key reason utilities are often willing to decouple or even leading proponents of the proposals is because the costs of building a power plant has risen dramatically. A 500- megawatt coal-fired plant that cost $1 billion just a few years ago might cost $1.5 billion today, industry experts say. Add to that growing uncertainty about future costs. Global- warming legislation could put a price of $ 30 per ton on carbon-dioxide emissions from power plants. That could make coal, the cheapest power today, more costly. Another factor is the rising community opposition to coal-fired power plant construction.
In North Carolina, where regulators recently refused a Duke Energy Corp. proposal to build a power plant, the company has instead put forward a controversial decoupling proposal. The plan would pay the company to meet efficiency standards, although consumer advocates and even environmental groups question whether it’s a good deal for ratepayers. In fact, some consumer advocates have major reservations about decoupling overall. "Unfortunately, we’re seeing utilities trying to use decoupling as a blank check," says Charles Acquard, executive director of the National Association of State Utility Consumer Advocates in Silver Spring, Md. "We’re not absolutely opposed to decoupling. It’s how you do it that’s critical.\

Which of the following gives the best definition of the expression "to stand tradition on its head" (para. 1)

A.To criticize tradition.

B.To go against tradition.

C.To carry forward tradition.

D.To integrate tradition.

单项选择题