Easy Mathematics

A target is an object used in various shooting sports to test the accuracy of various firearms (pistols, darts, bows and arrows, etc.). The center of the target is called the bullseye, and shooters try to make the bullet land as close to the bullseye as possible. The image below shows the standard five-color ten-ring target used in World Archery competitions, with a diameter of 80cm. The scores from the outermost ring to the bullseye range from 1 to 10. Assuming that an arrow is equally likely to land at any point on the target a) If a shooter can obtain all scores from 1 to 10 with equal probability in one shot, find the radius r of the bullseye. b) Assume the spacing between each ring is the same. A shooter shoots the target independently three times, obtaining a score X. Find the expected value of X.

Randomly choose 2 numbers in the interval [0, 1]. Determine the probability that their product is more than 0.4

In a farming simulation game, an animal has equal chance to produce a product at anytime between 30 and 40 second after you fed them. Assuming a player feeds animal immediately after a game start or the animal produced product. a) When you fed an animal, determine the probability that you receive 2 product within 1 minute 10 seconds. b) When you fed 5 animals, what is the expected number of product you will receive within 38 seconds? c) At the beginning of a game, a player has 20 chickens which produce eggs, each player is required to receive 23 eggs within t seconds, otherwise he loses the game. i) When t = 70, determine the probability that the player loses the game. ii) You should ensure that each player has at least 95% of winning chance, determine the least integer value of t that satisfies the requirement.

Gao Kao 2026 (2) 新高考二卷

Gao Kao 2026 （1） 新高考一卷

Recently, there is a popular moral dilemma problem: Suppose there are two colors of red and blue pills for people to choose from. If more than 50% of the people choose blue, all of them will survive; if more than 50% of the people choose red, all the blue side will die and all the red side will survive. There are nine people involved in this question, assuming that all nine people randomly selected a pill. Find the expectation on the number of people who will survive in the end.

An extend from past year question!

Long time no see 🤪