问题 解答题

甲、乙两人参加一次英语口语考试,已知在备选的10道试题中,甲能答对其中的6题,乙能答对其中的8题。规定每次考试都从备选题中随机抽出3题进行测试,至少答对2题才算合格,

(Ⅰ)求甲答对试题数ξ的概率分布及数学期望;

(Ⅱ)求甲、乙两人至少有一人考试合格的概率。

答案

解:(Ⅰ)依题意,甲答对试题数ξ的概率分布如下:

甲答对试题数ξ的数学期望Eξ=

(Ⅱ)设甲、乙两人考试合格的事件分别为A、B,

则P(A)=

P(B)=

因为事件A、B相互独立,

∴甲、乙两人考试均不合格的概率为

∴甲、乙两人至少有一人考试合格的概率为

答:甲、乙两人至少有一人考试合格的概率为

问答题
单项选择题

Washington, DC has traditionally been an unbalanced city when it comes to the life of the mind. It has great national monuments, from the Smithsonian museums to the Library of Congress. But day-to-day cultural life can be thin. It attracts some of the country’s best brains. But far too much of the city’s intellectual life is devoted to the minutiae of the political process. Dinner table conversation can all too easily turn to budget reconciliation or social security.

This is changing. On October 1st the Shakespeare Theatre Company opened a 775-seat new theatre in the heart of downtown. Sidney Harman hall not only provides a new stage for a theatre company that has hitherto had to make do with the 450-seat Lansburgh Theatre around the corner. It will also provide a platform for many smaller arts companies.

The fact that so many of these outfits are queuing up to perform is testimony to Washington’s cultural vitality. The recently-expanded Kennedy Centre is by some measures the busiest performing arts complex. But it still has a growing number of arts groups which are desperate for mid-sized space down- town. Michael Kahn, the theatre company’s artistic director, jokes that, despite Washington’s aversion (厌恶) to keeping secrets, it has made a pretty good job of keeping quiet about its artistic life. The Harman Centre should act as a whistle blower.

Washington still bows the knee to New York and Chicago when it comes to culture. But it has a good claim to be America’s intellectual capital. It has the greatest collection of think-tanks on the planet, and it regularly sucks in a giant share of the country’s best brains. Washington is second only to San Francisco for the proportion of residents twenty-five years and older with a bachelor’s degree or higher.

Washington’s intellectual life has been supercharged during the Bush years, despite the Decider’s aversion to ideas. September 11th, 2001, put questions of global strategy at the center of the national debate. Most of America’s intellectual centers are firmly in the grip of the left-liberal establishment. For all their talk of "diversity" American universities are allergic to a diversity of ideas. Washington is one of the few cities where conservatives regularly do battle with liberals. It is also the center of a fierce debate about the future direction of conservatism.

The danger for Washington is that this intellectual and cultural renaissance will leave the majority of the citizens untouched. The capital remains a city deeply divided between over-educated white itinerants and under- educated black locals. Still, the new Shakespeare theatre is part of job-generating downtown revival. Twenty years ago downtown was a desert of dilapidated(破旧的) buildings and bag people. Today it is bustling with life. If Washington is struggling to fix the world, at least it is making a reasonable job of fixing itself.

According to the text, which of the following statements is correct()

A. sidney Harman hall provides a new stage for Shakespeare Theatre Company

B. michael Kahn is the artistic director of the expanded Kennedy Centre

C. lansburgh Theatre is in the heart of downtown area in Washington

D. many smaller arts groups are desperate for mid-sized space downtown