As shown in the figure, there is a circle with a radius of 1cm in the rectangular ABCD with a length of 12cm and a width of 10cm on the plane (the center is at the diagonal intersection of the rectangle). What is the probability that a coin with a radius of 1cm will not collide with the circle if it is randomly thrown into the rectangle (the coin falls completely into the rectangle)? .

answer

Answer analysis: If a coin falls in a rectangle, the center of the coin should fall in a rectangle with a length of 12cm and a width of 10cm, and the coin has nothing in common with the small circle, and the distance between the center of the coin and the center of the small circle is greater than 2. First, find out the area where the coin falls in the rectangle, then find out the area where the coin does not intersect with the small circle after falling, and substitute it into the probability calculation formula of geometric probability.

Solution: solution: remember that "the coin did not collide with the circle o" is event a.

Coins should fall in a rectangle, and the center of coins should fall in a rectangle with a length of 10cm, a width of 8cm and an area of 80cm2.

There is no public dot, which means that the center of the coin is more than 2cm away from the center.

Make a circle with a radius of 2cm with O as the center, and the center of the coin is outside the circle, then the coin and the small circle with a radius of 1cm have nothing in common.

So the probability of having something in common is =,

Then the probability of no common point is p (a) = 1-.

So the answer is: 1-.

Comments: This topic mainly investigates the application of geometric probability calculation formula. The key to solve the problem is to determine the region that meets the conditions in the image.