问题 解答题

已知直线l1:x-2y-1=0,直线l2:ax-by+1=0,其中a,b∈{1,2,3,4,5,6}.

(1) 求直线l1与l2相交的概率;

(2) 求直线l1与l2的交点位于第一象限的概率.

答案

(1)  (2)

(1) 直线l1的斜率k1,直线l2的斜率k2.设事件A为“直线l1与l2相交”.a,b∈{1,2,3,4,5,6}的总事件数为(1,1),(1,2),…,(1,6),(2,1),(2,2),…,(2,6),…,(5,6),(6,6)共36种.若l1与l2相交,则l1∥l2,即k1=k2,即b=2a.满足条件的实数对(a,b)有(1,2),(2,4),(3,6)共三种情况.所以P(A)=.

(2) 设事件B为“直线l1与l2的交点位于第一象限”,由于直线l1与l2有交点,则b≠2a.联立方程组解得 ∵l1与l2的交点位于第一象限,∴

∵  a、b∈{1,2,3,4,5,6},∴  b>2a.∴ 总事件数共36种,满足b>2a的事件有(1,3),(1,4),(1,5),(1,6),(2,5),(2,6),共6种,∴  P(B)=

单项选择题 A1/A2型题
单项选择题

When Dave was eighteen, he bought a secondhand car for 200 so that he could travel to and from work more (1) than by bus. It worked quite well for a few years, but then it got so old, and it was costing him (2) much in repairs that he decided that he had better (3) it.

He asked among his friends to see if anyone was particularly (4) to buy a cheap car, but they all knew that it was falling to pieces, so (5) of them had any desire to buy it. Dave’s friend Sam saw that he was (6) when they met one evening, and said, "What’s (7) , Dave"

Dave told him, and Sam answered, "Well, what about advertising it in the paper You may (8) more for it that way than the cost of the advertisement!" Thinking that Sam’s (9) was sensible, he put an advertisement in an evening paper, which read "For sale: small car, (10) very little petrol, only two owners. Bargain at 50. " For two days after the advertisement first appeared, there was no (11) . But then on Saturday evening he had an enquiry. A man rang up and said he would like to (12) him about the car. "All right, " Dave said, feeling happy. He asked the man whether ten o’clock the next morning would be (13) or not. "Fine, " the man said, "and I’ll (14) my wife. We intend to go for a ride in it to (15) it. "

The next morning, at a quarter to ten, Dave parked the car in the square outside his front door, (16) to wait there for the people who had (17) his advertisement. Even Dave had to (18) that the car really looked like a wreck. Then, soon after he had got the car as clean (19) it could be, a police car stopped just behind him and a policeman got out. He looked at Dave’s car and then said, "Have you reported this (20) to us yet, sir\

20()

A.bargain 

B.sale 

C.accident 

D.result