Let the included angle from point A to the positive direction be: b, then b also obeys the uniform distribution of (0, 180) u (0, 180), the new distance is: 200sin(a)/sin(b), and the probability of the problem is:
200 sin(a)/sin(b)& lt; The probability of 200 is recorded as p (200 sin (a)/sin (b).
p(200 sin(a)/sin(b)& lt; 200)= P(sin(a)/sin(b)& lt; 1)= P(sin(a)& lt; Sin(b)). Since A and B obey the same distribution, the distribution of sin(a) and SIN (b) is exactly the same, so the above probability must be: 0.5.