Easy Mathematics
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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.
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
