Problem: You're playing a video game, where you select a missile and ?re it at 1 of 4 targets A, B, C, and D, chosen uniformly at random. There are 4 green missiles, 3 blue missiles, 2 red missiles, and 1 black missile. You select a missile uniformly at random, and each time, it is replaced immediately by a missile of the same color. The green missile has an accuracy of 25%, the blue missile has an accuracy of 50%, the red missile has an accuracy of 75%, and the black missile has an accuracy of 100%. If Target A is hit, you get 50 points; if Target B is hit, you get 70 points; if Target C is hit, you get 40 points; and if Target D is hit, you get 60 points. If you miss the target, you get no points.

Required:

Question 1: What is your expected number of points after 12 missiles are ?red?

Question 2: You ?re missiles until you hit your ?rst target. What is the expected number of missiles you ?re?

Question 3: What is the variance of the number of points you earn from ?ring a single missile?