D Question 1 5 pts Let A and B be events with P(A) = 0.5 and P(B) = 0.4. a) If P(A and B) = 0.3, find P(A or B). b) If event A and event B are mutually exclusive, find P(A or B). c) Find P(B"). d) If event A and event B are independent events. Find P(A and B). e) If P(B|A) = 0.2. Find P(A and B).D Question 2 2 pts A lot of 1000 components contains 300 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Find P(B|A). 300/1000 O 299/999 O 298/1000 O 2/300Question 3 8 pts In the game of tic-tac-tee, if all moves are performed randomly the probability that the game will end in a draw is 0.127. Suppose 12 random games of tic-tac-toe are played. a) What is the probability that at least one of them will end in a draw? '(round to the nearest theusandths... i.e. 3 decimals places) b) What is the probability that exactly six of them will end in a draw? ' [round to the nearest thousandths... i.e. 3 decimals places) c] What is the probability that less than ve of them will end in a draw? '(round to the nearest thousandths... i.e. 3 decimals places) d) What is the probability that two or three of them will end in a draw? '(round to the nearest thousandths... i.e. 3 decimals places) D Question 4 1 pts An investor is considering a $25,000 investment in a start-up company. She estimates that she has probability 0.15 of a $20,000 loss, probability 0.1 of a $30,000 profit, probability 0.25 of a $40,000 profit, and probability 0.5 of breaking even (a profit of $0). What is the expected value of the profit? D Question 5 5 pts A committee consists of 10 women and eight men. Three committee members will be chosen as officers. Round all answers to the nearest thousandths place. (3 decimal places) a) How many different choices are possible? b) How many different choices are possible if all the officers are to be women? c) How many different choices are possible if all the officers are to be men? d) What is the probability that all the officers are women? e) What is the probability that at least one officer is a man?D Question 6 4 pts A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). a) List all the outcomes of the sample space. b) Assuming the outcomes to be equally likely, find the probability (as a fraction) that both answers are "C". c) Assuming the outcomes to be equally likely, find the probability (as a fraction) that at least one answer is a "C". Upload a PDF of your answers. Upload Choose a File