discrete maths

AST21111 Assignment 3 Question 9 [10 marks] A company sends millions of people an entry form for a lucky-draw accompanied by an order form for magazine subscriptions. There will be 3 winners in the lucky-draw. The first, second, and third prizes of the lucky-draw are $10,000,000, $1,000,000, and $50,000, respectively. In order to qualify for a prize, a person is not required to order any magazines but has to spend $6 for the delivery services of returning the entry form. At the close of the game, 30 million entry forms are returned. What is the expected gain or loss per a returned entry form? AST21111 Assignment 3 Question 10 [15 marks] Two different factories both produce a certain automobile part. The probability that a component from the first factory is defective is 2%, and the probability that a component from the second factory is defective is 5%. In a supply-batch of 180 of the parts, 100 were obtained from the first factory and 80 from the second factory. a. What is the probability that a part chosen at random from the supply- batch of 180 of the parts is from the first factory? b. What is the probability that a part chosen at random from the supply- batch of 180 of the parts is from the second factory? C. What is the probability that a part chosen at random from the supply- batch of 180 of the parts is defective? d. If a randomly chosen part from the supply-batch of 180 of the parts is defective, what is the probability that it came from the first factory