问题 解答题

乒乓球比赛规则规定:一局比赛,双方比分在10平前,一方连续发球2次后,对方再连续发球2次,依次轮换,每次发球,胜方得1分,负方得0分。设在甲、乙的比赛中,每次发球,发球方得1分的概率为0.6,各次发球的胜负结果相互独立。甲、乙的一局比赛中,甲先发球。

(1)求开始第4次发球时,甲、乙的比分为1比2的概率;

(2)ξ表示开始第4次发球时乙的得分,求ξ的期望。

答案

解:记为事件“第i次发球,甲胜”,i=1,2,3,

(1)事件“开始第4次发球时,甲、乙的比分为”为

由互斥事件有一个发生的概率加法公式得

即开始第次发球时,甲、乙的比分为的概率为0.352。

(2)由题意

=0.408;

所以

单项选择题

The Erie Canal was the first important national waterway built in the US. It crossed New York from Buffalo on Lake Erie Troy to Albany on the Hudson River. It joined the Great Lakes with the Atlantic Ocean. The canal served as a route over which industrial goods could flow into the west, and materials could pour into the east. The Erie Canal helped New York develop into the nation’s largest city.

The building of the canal was paid for entirely by the state of New York. It cost $ 7 143 789, but it soon gained its price many times over. Between 1825, when the canal was opened, and 1882, when toll charges were stopped, the state collected $121 461 891.

For a hundred years before the Erie was built, people had been talking about a canal which could join the Great Lakes and the Atlantic Ocean. The man who planned the Erie Canal and carried the plan through was De Witt Clinton. Those who were against the canal laughingly called it "Clinton’s Ditch". Clinton talked and wrote about the canal and drew up plans for it. He and Governor Morris went to Washington in 1812 to ask for help for the canal, but they were unsuccessful.

Clinton became governor of New York in 1817, and shortly afterwards, on July 4, 1817, broke ground for the canal in Rome, N. Y. The first part of the canal was completed in 1820. As the canal grew, towns along its course developed fast. The length of the canal is 363 miles.

We can see that the Erie Canal ().

A. joined the Great Lakes together

B. crossed New York from north to south

C. played an important part in developing New York City

D. was the first waterway built in the US

多项选择题