ny Problem set 1. A modified roulette wheel has 26 numbers (1 through 24, 0, and 00). As the wheel spins, a ball is rolled on the wheel and bets are placed as to where the ball will land. You can bet on a single number, as well as on 2, 3, 4, 5, 6, 12 numbers. What are the odds in favour of winning if you bet on an even number? Note: 0 and 00 are not considered even numbers. (3) Odds in favour = P(A) 2 = 12 P(A) 26 - 12 = 14 P( A') -PIA'S = 12 . The odds 2. Your friend has an 8-letter password for her e-mail account. 14 favouris 6 a) What is the probability that if you guess her password, you will be correct? = 6/7 (*Note: The same letter may be used multiple times and the password is not case sensitive ) ( 2 ) 26 letters n( A) = 26 P8 = 156 227, 5 P(A) = 1 A - > probability of getting password 156227 .5 = 0.00000 064 b) Many websites require that your password be at least 8 characters long and include at least one number and one letter. If you knew the password were 8 characters long, what is the probability that you would guess a password in this case? (assume that no special characters are used, and that the password still isn't case sensitive) (4) 3. In a contest, five players qualify for a chance to win a car. To wha contestant must choose the correct key to start the car, from a group of 5 keys. Chestants are randomly selected to choose a key, one at a time and try it. The 9. hige ends when someone starts the car. Determine which player, if any, has the no chance of winning the car: the first to choose, the last to choose, or someone "themiddle Show all work and explain your reasoning. (4) 4. A computer screen is divided into a 16 by 9 grid with grid points dellheyby or pairs, using whole numbers from (0, 0) to (16, 9). A segment is dial, joined randomly chosen points. What is the probability that the line segment is mylo (4) 5. What is the probability of being dealt five cards from a standard deck and get three queens along with another pair (three queens plus two other cards of the value). (4)