10 Air Meter Pistol Event. In a 10-Metre-Air-Pistol event, a 4.5 mm caliber air gun is shot from a distance of 10 meters into a circular target with a 6 feet radius whose center we call the origin. The program consists of 60 shots within 105 minutes for men. The outcome of this random experiment is a shot on the target. The shooter scores 10 points if he hits the bull’s eye, which is a disk with radius of 1- footcentered at the origin; he scores 5 points if he hits the ring with inner radius of 1 foot and outer radius of 3 feet centered at the origin; and he scores 0 points if he shoots anywhere outside. Assume that the shooter will actually hit the target. For one shot, let S be the score.

a. Obtain and interpret the probability distribution of the random variable S. (Hint: The area of a disk is the square of its radius times π.)

b. Use the special addition rule and the probability distribution obtained in part

(a) to determine and interpret the probability of each of the following events:{S = 5};{S > 0};{S ≤ 7};{5 < S ≤ 15};

{S < 15}; and {S < 0}.