This is in Statistics all about Random Variable. This is only multiple choice. Provide necessary solution for each items. Thank you and Godbless. Follow the numbering.

8. Tony works on a tire factory. The random vairable X" indicates the number of defective tires that he produced on a random day and has the probability distribution shown in the table below. 2 3 4 5 P(X =x) 0.48 0.36 0.12 0.04 Find the probability that tony produce at least 3 defective tires tomorrow. Hint: This is equivalent to P(X2 3). A) 0.16 C) 0.12 B) 0.36 D) 0.52 9. Five thousand lottery tickets are sold for 50 pesos each. One ticket will win 50,000 pesos, two tickets will win 25,000 pesos each, and 10 tickets will win 5,000 pesos each. Let A" denote the net gain from the purchase of a randomly selected ticket. After constructing the probability distribution for X, find P(X = 4950). Hint: The net gain is the winning prize minus ticket price. A) 4987/5000 C) 1/5000 B) 1/500 D) 1/250 10. Five thousand lottery tickets are sold for 50 pesos each. One ticket will win 50,000 pesos, two tickets will win 25,000 pesos each, and 10 tickets will win 5,000 pesos each. Let X denote the net gain from the purchase of a randomly selected ticket. What is the expected value E(X)? A) -25 C) -30 B) -20 D) -15