I need assistance with the following questions:

1. A full house in poker is a hand where three cards share one rank and two cards share another rank. How many ways are there to get a Full-house? What is the probability of getting a full-house? 2. There are 3 arrangements of the word DAD, namely DAD, ADD, and DDA. How many arrangements are there of the word PROBABILW 3. {a} How many ways can you arrange the letters in the word STATISTICS? (e.g. SSSTTTIIAC counts a one arrangement.) {b} If all arrangements are equally likely, what is the probabilitiy the two *i's are next to each other. 4. There are six men and seven women in a ballroom dancing class. If four men and four women are chosen and paired off, how many pairings are possible? 5. Suppose you pick two cards from a deck of 52 playing cards. What is the probability that they are both queens? . Suppose that there are ten students in a classroom. What is the probability that no two of them have a birthday in the same month? 7. 2i} politicians are having a tea party, (i Demmrats and 14 Republicans. To prepare, they need to choose: 3 people to set the table, 2 people to boil the water, H people to make the scones. Each person can only do 1 task. [Note that this doesnlt add up to 2G. The rest of the people don't help.) (a) In how many different ways can they choose which people perform thme tasks? {b} Suppose that the Democrats all hate tea. If they only give tea to 1'1} of the ED people, what is the probability that they only give tea to Republicans? {c} If they only give tea to ll] of the EU people, what is the probability that they give tea to '9 Republicans and 1 Democrat? E. Let A and B be two events. Suppose the probability that neither A or B occurs is 23'3. What is the probability that one or both occur? 9. Let C and .D be two events with P{C] = 0.25, PLO} = 13.45, and Flt? n D] = I11. What is FfC'cn D)? 10. You roll a four-sided die 3 times. For this problem we'll use the sample space with 6-1. equally likely outcomes. [at] Write down this sample space in set notation. 1 (b) List all the outcomes in each of the following events. {i} A = +li'ssastly 2 of the 3 rolls are fonrs1 {ii} B = 'At least 2 of the 3 mils are fours' [iii] C = *Esactly 1 of the second and third rails is a 4' {iv} A I'l C 11. Suppose we have 8 teams labeled T1, ..., Ts. Suppose they are ordered by placing their names in a hat and drawing the names out one at a time. (a) How many ways can it happen that all the odd numbered teams are in the odd numbered slots and all the even numbered teams are in the even numbered slots? (11} 1What is the probability of this happening? 12. (Taken from the book by Deklring et. a]. problem 4.9} The space shuttle has 6 {Ii-rings [these were involved in the Challenger disaster}. When launched at 31\" F! each tiring has a probability of failure of 11.013? {independent of whether other Ci-rings fail). (a) What is the probability that during 23 launches no (fl-ring will failI but that at least one (Ii-ring will fail during the 24th launch of a space shuttle? (b) What is the probability that no Gring fails during 24 launches? 2 Conditional Probability and Bayes' Theorem 13. More cards! Suppose you want to divide a 52 card deck into four hands with 13 cards each. 1What is the probability that eanh hand has a king? 14. Suppose you are taking a multiple-choice test with s Choioes for sash question. In answering a question on this test1 the probability that you know the answer is 1:. If you don"t know the answer1 you choose one at random. What is the probability that you knew the answer to a questionl given that you answered it oorrectly? 15. Corrupted by their powerI the judges running the popular game show America 's Nest Top Mathematician have been taking bribes from many of the mntestants. Each episode1 a given contestant is Either allowed to stay on the show or is kicked o. If the contestant has been bribing the judges she will be allowed to stay with probability 1. If the contestant has not been bribing the judgesl she will be allowed to stay with probability 1f-3. Suppose that lid of the contestants have been bribing the judges. The same contestants bribe the judges in both rounds. Le.I if a contestant bribes them in the rst round, she bribes them in the second round too (and vice versa). (a) If you pick a random contestant who was allowed to stay during the rst episode, what is the probability that she was bribing the judges? (11} If you pick a random contestant, what is the probability that she is allowed to stay during both of the rst two episodes