Answer the following

1. Which of the following represents the mean value of a discrete random variable? A. Expected value C. Standard deviation B. Median D. Variance For numbers 2-3, refer to the table below: x 2 4 6 8 P(x) 0. 12 0.29 0.24 0.35 2. Which of the following is the correct formula to find the expected value of the probability distribution? A. E(x) = E[x . P(x)] C. E(x) = [x2 . P(x)] - u2 B. E(x) = E[x2 . P(x)] D. E(x) = VE[x2 . P(x)] - u2 3. What is the mean or the expected value of the given probability distribution? A. 4.85 B. 5.64 C. 6.32 D. 7.12 For numbers 4-6, refer to the following: You buy one P500.00 raffle ticket for a prize of new Toyota Wigo car valued at P675, 000.00. Two thousand tickets are sold. 4. What is the probability that you will win the prize? A. 1 B. = 1 1 500 C. 2000 D. 675000 5. If X denotes the net gain from the purchase of a randomly selected ticket. Which of the following tables of values shows the probability distribution of X? X 675,000 -500 105A. P(x) 1999 C. X 674,500 -500 2000 2000 P(x) 1999 2000 2000 X 675,000 X 674,500 500 B. 500 P(X) 1999 D. P(x) 1999 2000 2000 2000 2000 6. What is the mean or the expected value for those who will buy the tickets? A. -162.50 B. -162.25 C. 162.25 D. 162.50 For numbers 7-8, refer to the following: One thousand tickets are sold for P 10.00 each. One ticket will win P2,000.00, two tickets will win P 1,000.00 each and four tickets will win P500.00 each. 7. What is the probability of winning any amount in the purchase of two tickets? A. 1 1000 B. D. 7 1000 C. 1000 1000 8. What is the probability of losing in the purchase of two tickets? A. 2 500 998 D. 999 1000 B. 1000 C. 1000 1000 For numbers 9-11, refer to the following: A roulette wheel in a fiesta carnival has the numbers 1 through 50. If you bet P5.00, you will have a chance to win a kitchen utensil worth P200.00. 9. If X denotes the net gain from taking a chance to bet on a randomly selected number. Which of the following tables of values shows the probability distribution of X? A. X 195 -5 X 50 -5 P(x) 49 P(x) 1 199 50 50 200 200 B. X 5 -5 D. X 200 5 P(x) P(x) 5 200 200 10. What is the mean or the expected value for those who take a bet? A. - 1.8 B. - 1 C. -0.95 D. -0.5 11. How much the organizer will earn if 100 games will be played such that each number has a bet of P5.00? A. P2,000.00 B. P3,000.00 C. P4,000.00 D. P5,000.00 For items 12-13, refer to the following: Good Hands is a car insurance company who offers to pay P600,000.00 if a car is destroyed beyond repair due to an accident. This insurance policy cost P25,000.00 per year and the probability that the company will need to pay the amount of insurance is 0.003. 12. What is the probability that the company will NOT pay any amount to its client within a year? A. 0.003 B. 0.250 C. 0.500 D. 0.997 13. What is the expected value of the insurance to its buyer? A. Each policyholder expects to lose P20,000.00 every year. B. Each policyholder expects to lose P22,500.00 every year. C. Each policyholder expects to lose P23,200.00 every year. D. Each policyholder expects to lose P25,000.00 every yearFor items 14 to 15, refer to the following: A life insurance company will sell a P500,000.00 five-year term life insurance policy exclusive for police enforcers for a premium of P1,000.00. The chance that a police enforcer will survive in 5 years is 99.95%. 14. What is the probability that a police enforcer will NOT survive in five- years? A. 0.05 B. 0.005 C. 0.005 D. 0.0005 /15. What is the expected value to the company of a single policy? A. P550.00 B. P650.00 C. P750.00 D. P850.00What's New GAME OF CHANCE .Read the conversation below and answer the questions that follow. Oh no! I do understand but if you want to take a slum; I have here 5 rafe tickets om of 1000 released tickets Which cost P100.00 each. If you will be lucky enough, you'll get a 32-inch LED Television worth 'P15',000.00. Our television set is 'no longer mctional and I. need to buy a new one. But the problem is I don't have enough budget for that. ' Hey Romulo I have a problem. , 0k, so what s your problem my 'iend? That's a good deal and the prize is so exciting! But I need to check: my budget before buying a ticket. Thanks for informing me. I'll just call you when I am ready to buy, _ By the way, when is the rafe date? \\ ' It- Will be 10 days 'on-i now. ' 'You still have. time to decide, , ' just oall' me if you already '. ' have yOur decision. Questions: 1. If you are Cardo, would you buy a raffle ticket? Why? 2. If Cardo decided to buy five tickets, what is the probability that he would win the prize if 1000 tickets were sold? What is the probability that Cardo will lose the bet? 3. How much money will Cardo gain if he wins the prize? 4. How much money will be wasted if he will not win the prize and he buy one ticket? 5. What if 1000 tickets were purchased by different individuals, what is the expected value of buying one ticket? 6. How would you describe Romulo as a friend?What I Can Do Raffle for a Cause! Things to do: Make a plan for a Christmas raffle bonanza in which the PWD (Person with Disability) will be the beneficiaries. The plan should consist of the number of tickets to be sold, the amount per ticket, and the number of winners and their corresponding prizes. Let X be the random variable representing your net gain per ticket, and compute the expected value of X and the net gain if all tickets will be sold out. Also, using your creativity prepare a sample of your ticket. You may use the sample guide to complete your task. Name of Project Brief Description Number of tickets to be sold Price of ticket to be sold Winners and prizes: Expected Value of X: Please show the probability distributions and your solution) Net Gain of the Project: Sample Ticket