Assignment 14 Chapter 4 Probability models pp 220 232 Homework 1 3 4 17 4 18 4 19 4 25 4 26 4 32 Probability model sample space S with probabilities P A description of a random phenomenon in the language of mathematics Event an outcome or set of outcomes a subset of the sample space S Complement of A Ac Ac 1 A Disjoint two sample spaces have no elements in common Example even numbers and odd numbers are disjoint They have no elements in common Independent one event does not influence subsequent events Example Rolling a die Rolling a die once has no influence on subsequent rolls Basic rules 0 P A 1 for any event A P S 1 1 If A and B are disjoint then P A or B P A P B 2 Complement rule for any event A P Ac 1 P A 3 Multiplication rule if A and B are independent then P A and B P A x P B AND FOLLOWED BY Practice with the rules 1 If A and B are disjoint then P A or B P A P B a When rolling a single die what is the probability of rolling a 3 or a 6 b When rolling two dice what is the probability of rolling a 4 or a 7 or an 11 This problem will require you figuring out what is the sample space What are the total number of ways you can roll a 2 a 3 a 4 etc 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6 2 Complement rule for any event A P Ac 1 P A a If 17 of people who live in the United States speak Spanish what percent do not speak Spanish For this problem assume that no one is bilingual b If 12 of the population of a country are Hispanic and 23 are Asian what percent of the population is some other ethnicity neither Hispanic or Asian For this problem assume that no one is of mixed ethnicity 3 Multiplication rule if A and B are independent then P A and B P A x P B a If I am rolling a single die what is the probability that I will roll a 2 and then roll a 6 b When rolling two dice what is the probability of rolling a 4 followed by a 7 followed by an 11 Your work in problem one can assist you here 4 17 page 232 For each of the following questions define a sample space for the associated random phenomenon Explain your answers Be sure to specify units if that is appropriate a Will it rain tomorrow b How many times do you tweet in a typical day c What are the ages of your Facebook friends d What are the majors for students at Burman 4 18 page 232 For each of the following situations state the probability rule or rules that you would use and apply it or them Write a sentence explaining how the situation illustrates the use of the probability rules a The probability of event A is 417 What is the probability that event A does not occur b A coin is tossed four times The probability of zero heads is 1 16 ALL TAILS and the probability of zero tails is 1 16 ALL HEADS What is the probability that all four tosses will result in the same outcome that is all heads or all tails c Refer to part b What is the probability that there is at least one head and at least one tail d The probability of event A is 4 and the probability of event B is 8 Events A B are disjoint Can this happen e Event A is very rare Its probability is 0 04 Can this happen 4 19 page 232 For each of the following situations explain why you think that the events are equally likely or not equally likely Explain your answer a The outcome of the next tennis match for Sloane Stevens is either a win or a loss better google Sloan Stevens b You roll a fair die and get a 3 or a 4 c You are observing turns at an intersection You classify each turn as a right turn or a left turn d For college basketball you record the number of times the home team wins and the number of times the home team loses 4 25 page 233 Distribution of blood types in the US a What is the probability of AB blood in the US b Maria has type B blood She can safely receive blood transfusions from people with blood types O and B What is the probability that a randomly chosen person from the US can donate blood to Maria 4 26 page 233 Choose a person from the US and a person from Ireland at random independently of each other a What is the probability both have type O blood b Probability they both have the same blood types 4 32 page 234 Roulette wheel 38 slots 0 and 00 are green of the remaining 36 18 are red and 18 are black The dealer spins the wheel and at the same time rolls a ball in a groove above the wheel in the opposite direction The ball is equally likely to fall in any of the 38 slots a What is the probability of landing in one slot b What is the probability of landing on red c A column bet identifies landing in a slot that is a multiple of 3 e g 3 6 9 What is your probability of winning a column bet