1.Suppose two dice are tossed. For each die, it is equally likely that 1,2,3,4,5 or 6 dots will appear.

(a)What is the probability that the sum of numbers showing up on the pair of dice is 4 or 9?

(b)What is the probability that the sum of numbers showing up on the pair of dice equals a number other than 5 or 10?

(c)Are the events E1= first die shows a 4, and E2=sum of numbers showing up on the pair of dice is 7, independent events?

18.12

(a)What is the probability of any of the 38 possible outcomes?

(b)If you bet on red, you win if the ball lands in a red slot. What is the probability of winning?

C)The slots numbers are laid out on board on which gamblers place their bets. One column of numbers on the board contains all multiples of 3, that is 3,6,9,36. What is the probability of winning?

18.16

(a)What is the probability that the poll gets a sample in whichmore than71% of the people think that airplane would be safer if passengers were banned from carrying on board any luggage, including purses, computers and brief cases?(10 points)

(b)What is the probability of getting a sample that misses the truth (68%) by 3.0% or more?(10 points)use"68-95-99.7"rule.

18.12 Roulette. A roulette wheel has 38 slots, numbered 0, 00, and 1 to 36. The slots 0 and 00 are colored green, 18 of the others are red, and 18 are black. The dealer spins the wheel and at the same time rolls a small ball along the wheel in the opposite direction. The wheel is carefully balanced so that the ball is equally likely to land in any slot when the wheel slows. Gamblers can bet on various combinations of numbers and colors. (a) What is the probability of any one of the 38 possible outcomes? Explain your answer. (b) If you bet on \"red,\" you win if the ball lands in a red slot. What is the probability of winning? (0) The slot numbers are laid out on a board on which gamblers place their bets. One column of numbers on the board contains all multiples of 3, that is, 3, 6, 9,. . ., 36. You place a \"column bet\" that wins if any of these numbers comes up. What is your probability of winning? 18.16 Airplane safety. Suppose that 68% of all adults think that airplanes would be safer places if airline passengers were banned from carrying on board any luggage, including purses, computers, and briefcases. An opinion poll plans to ask an SRS of 1023 adults about airplane safety. The proportion of the sample who think that airplanes would be safer if passengers were banned from carrying on board any luggage, including purses, computers, and briefcases, will vary if we take many samples from this same population. The sampling distribution of the sample proportion is approximately Normal with mean 0.68 and standard deviation about 0.015. Sketch this Normal curve and use it to answer the following questions. (a) What is the probability that the poll gets a sample in which more than 71% of the people think that airplanes would be safer if passengers were banned from carrying on heard any luggage, including purses, computers, and briefcases? (b) What is the probability of getting a sample that misses the truth (68%) by 3.0% or more