Probability problems in the third year of junior high school, probability problems in the third year

1. To make the equation have a real root, m>=n, when n=0, m has 4 cases; n=1,m has 3 cases; n=2,m has 2 cases. There are 9 cases, and the value of m and n is 4*3=12 cases, so the probability is 9 12 = 3 4.

2, this question should be the default probability of encountering a red light at each intersection is 1 2, Xiao Ming is not late There are two types of situations: 15 minutes to school, no red light, the probability is (1 2) 4=1 16;When you arrive at school in 16 minutes and encounter a red light, the probability is c4, 1*1 2*(1 2) 3=1 4. Therefore, the probability that Xiao Ming is not late is 1 16 + 1 4 = 5 16.

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Passing point C to the AB perpendicular line, the vertical foot is DTake e on dc so that de is equal to three-quarters of dcOver E as Fg parallel AB, F on AC, G on BC.

Then any point on the line break fg satisfies the area ratio equal to three-quarters, i.e., the eligible p will be at any point in the triangle fgc. Divide the area of the FGC by the area of the ABC to give you the probability of satisfying the condition. The area ratio is obvious, since the bottom and height are the original 1 4.

The area ratio of the nail is (1-3 4) squared. That is, the result is 1 16.

Make the high Cd on Ab, take a little F on Cd to make Cf than Fd 1 to 3, cross F as Ab parallel line AC, Bc to m, n

Then P falls in the triangle CMN to meet the requirements.

p=1/16

What is easy to make in this question is to directly use the ratio of the high to get 1 4

The waiter didn't lie.

Of the 1,500 people**, 781 prizes were drawn, with a winning rate of over 50.

The winning rate of the first prize is the probability of not winning.

The probability of the first 1500 people winning each draw is: (

The probability is still very high.

btw: Xiao Ming and his mother can draw 2 times and may not win the lottery, the probability of not winning (1 2) 2=1 4.

Probability of a draw (1 3) (1 3) + (1 3) (1 3) (1 3) 3!=1/9+2/9=1/3

A single win rate = (1 3) 3 * (c3 1) = 1 9 B single win rate = (1 3) 3 * (c3 1) = 1 9 C single win rate = (1 3) 3 * (c3 1) = 1 9 A B win rate = (1 3) 3 * (c3 2) = 1 9 A C win rate = (1 3) 3 * (c3 2) = 1 9 B C win rate = (1 3) 3 * (c3 2) = 1 9 Everyone has the same win rate (there is overlap).

1 3 draw rate 1 3

Fair play.

Of course it's fair, just draw a tree diagram.

From the meaning of the title, it can be seen that the display of the clock is a cycle of two and a half minutes, and in each two and a half minutes of time, there is half a minute of time to display time information, so the probability of Xiao Ming seeing the time is:

30 seconds (30 seconds + 2 minutes) = 30 150 = 1 5

The pattern displayed is 2 minutes (120 seconds) of school information, 30 seconds of time, 2 minutes (120 seconds) of school information, and 30 seconds of time,。。

Therefore, probability = 30 (30 + 120) = 1 5

The probability that Xiao Ming will be assigned to class (1) is 1 16, and the probability that Xiao Qiang will also be assigned to class (1) is also 1 16, and the probability that they are all assigned to class (1) is 1 16*1 16 = 1 256, but they are assigned to class (2) and class (3) 、......16) The probability of the class is 1 256, so the probability of them being placed in the same class is 1 256 * 16 = 1 16

Their chances of being assigned to each class are the same.

Xiao Ming is assigned to any class, and the probability is 1

Xiao Qiang and Xiao Ming are in the same class.

The probability is 1*1 16=1 16

The probability of Xiao Ming and Xiao Qiang's class A is 1 16 * 1 16 = 1 256 and there are 16 classes, so it is 16 * 1 16 * 1 16 = 1 16

Solution: p (take out the green ball) = 1-p (take out the yellow ball) = 1- 2 5= 3 5 There are green balls in the bag x3 5 18 The probability of taking out the green ball is 3 5. 2。Total balls.

There is a bag of red and black balls, they are of the same mass and shape, and there are 123 known red balls. There are 154 black balls, and I get one ball from them, what is the probability that I will get the red ball?

Answer: 123 277

For example, if you run a total of 20 times, then according to the probability, you will get 100 yuan 2 times (20 * (1 10)), get 50 yuan 4 times (20 * (1 5)), get 20 yuan 5 times (20 * (1 4)), then 20 times a total of 20 times get:

100*2 + 50*4 + 20*5 = 500 RMB.

The average is 500 20 = 25 yuan.

In fact, Xianghui faction should be: