Statistics and probability questions. Answer all.

Statistics and Probability questions . S, 1. you consult Joel the bookie as to the form in the 2130 at A year. He tells you that of 16 runners, The Favourite how probability or 20 of winning and the reminder each have probability of oros winning expecting desert fury, Which has a worse than the winning no chance of winning . What do you think of Joet's advice? 2. Suppose that for the of the standard type of all 2016 outcomes of a throw are equally likely. Denote the scores Obtained by X, X, and Xy' By counting outcomes in the events find @ P ( x, +x2+x3 . (bj p ( min ( x ,x2, x3) > i) fori = 1 , 2 ... 6 ( C ) p ( x , tx2t faj ?) P 3 . Count the number of distinct ways of putting 3 balls into 4 boxes when: MB. all boxes and balls are distinguishable. K BE " The boxes are different but balls are Identicale FD The balls are Jedentical . See if you can do the counting when there are in bills and and n boxes . 4 . A lucky dip at a school fete Contains loo packages of which Ho Contains tickets for prizes- Let x denotes Therprices you win when you draw out three of the packages. Find the probability density of X That is P ( x = ]) for each appropriate ? .7E-1 A bridge hand in which there is no card higher than a nine is called a Yarborough. Specify an appropriate sample space and determine the prob- ability of Yarborough when you are randomly dealt 13 cards out of a well- shuffled deck of 52 cards. 7E-2 Five dots are placed at random on a 8 x 8 grid in such a way that no cell contains more than one dot. Specify an appropriate sample space and determine the probability that no row or column contains more than one dot. 7E-3 Five people are sitting at a table in a restaurant. Two of them order coffee and the other three order tea. The waiter forgot who ordered what and puts the drinks in a random order for the five persons. Specify an appropriate sample space and determine the probability that each person gets the correct drink 7E-4 A parking lot has 10 parking spaces arranged in a row. There are 7 cars parked. Assume that each car owner has picked at a random a parking place among the spaces available. Specify an appropriate sample space and determine the probability that the three empty places are adjacent to each other. 7E-5 Somebody is looking for a top-floor apartment. She hears about two vacant apartments in a building with 7 floors en 8 apartments per floor. What is the probability that there is a vacant apartment on the top floor? 7E-6 You choose at random two cards from a standard deck of 52 cards. What is the probability of getting a ten and hearts? 7E-7 A box contains 7 apples and 5 oranges. The pieces of fruit are taken out of the box, one at a time and in a random order. What is the probability that the bowl will be empty after the last apple is taken from the box? 7E-8 A group of five people simultaneously enter an elevator at the ground floor. There are 10 upper floors. The persons choose their exit floors inde- pendently of each other. Specify an appropriate sample space and determine the probability that they are all going to different floors when each person randomly chooses one of the 10 floors as the exit floor. How does the answer change when each person chooses with probability = the 10th floor as the exit floor and the other floors remain equally likely as the exit floor with a probability of To each. 7E-9 Three friends and seven other people are randomly seated in a row. Specify an appropriate sample space to answer the following two questions. (a) What is the probability that the three friends will sit next to each other? 2 (b) What is the probability that exactly two of the three friends will sit next to each other? 7E-10 You and two of your friends are in a group of 10 people. The group is randomly split up into two groups of 5 people each. Specify an appropriate sample space and determine the probability that you and your two friends are in the same group. 7E-11 You are dealt a hand of four cards from a well-shuffled deck of 52 cards. Specify an appropriate sample space and determine the probability that you receive the four cards J, Q, K, A in any order, with suit irrelevant. 7E-12 You draw at random five cards from a standard deck of 52 cards. What is the probability that there is an ace among the five cards and a king or queen? 7E-13 Three balls are randomly dropped into three boxes, where any ball is equally likely to fall into each box. Specify an appropriate sample space and determine the probability that exactly one box will be empty. 7E-14 An electronic system has four components labeled as 1, 2, 3, and 4. The system has to be used during a given time period. The probability that component i will fail during that time period is f, for i = 1, ..., 4. Failures of the components are physically independent of each other. A system failure occurs if component 1 fails or if at least two of the other components fail. Specify an appropriate sample space and determine the