Problem 1ED: (A) Suppose that E and F are complementary events. Are E and F necessarily mutually exclusive?... Problem 2ED: Determine the smallest number n such that in a group of n people, the probability that 2 or more... Problem 1MP: Use the sample space in Example 1 to answer the following: (A) What is the probability of rolling an... Problem 2MP: Use the sample space in Example 2 to answer the following: (A) What is the probability that a sum of... Problem 3MP: What is the probability that a number selected at random from the first 140 positive integers is... Problem 4MP: A shipment of 40 precision parts, including 8 that are defective, is sent to an assembly plant. The... Problem 5MP: Use equation 3 to evaluate PE for n=4. Problem 6MP: (A) What are the odds for rolling a sum of 8 in a single roll of two fair dice? (B) If you bet $5... Problem 7MP: If in repeated rolls of two fair dice, the odds against rolling a 6 before rolling a 7 are 6 to 5,... Problem 8MP: Refer to Example 8. If a person from Springfield is selected at random, what is the (empirical)... Problem 1E: In Problems 1-6, write the expression as a quotient of integers, reduced to lowest terms. (If... Problem 2E Problem 3E: In Problems 1-6, write the expression as a quotient of integers, reduced to lowest terms. (If... Problem 4E: In Problems 1-6, write the expression as a quotient of integers, reduced to lowest terms. (If... Problem 5E: In Problems 1-6, write the expression as a quotient of integers, reduced to lowest terms. (If... Problem 6E: In Problems 1-6, write the expression as a quotient of integers, reduced to lowest terms. (If... Problem 7E: Problems 7-12 refer to the Venn diagram below for events A and B in an equally likely sample space... Problem 8E: Problems 7-12 refer to the Venn diagram below for events A and B in an equally likely sample space... Problem 9E: Problems 7-12 refer to the Venn diagram below for events A and B in an equally likely sample space... Problem 10E: Problems 7-12 refer to the Venn diagram below for events A and B in an equally likely sample space... Problem 11E: Problems 7-12 refer to the Venn diagram below for events A and B in an equally likely sample space... Problem 12E: Problems 7-12 refer to the Venn diagram below for events A and B in an equally likely sample space... Problem 13E: A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a... Problem 14E: A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a... Problem 15E: A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a... Problem 16E: A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a... Problem 17E: A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a... Problem 18E: A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a... Problem 19E: A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a... Problem 20E: A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a... Problem 21E: A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a... Problem 22E: A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a... Problem 23E: A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a... Problem 24E: A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a... Problem 25E: In a lottery game, a single ball is drawn at random from a container that contains 25 identical... Problem 26E: In a lottery game, a single ball is drawn at random from a container that contains 25 identical... Problem 27E: In a lottery game, a single ball is drawn at random from a container that contains 25 identical... Problem 28E: In a lottery game, a single ball is drawn at random from a container that contains 25 identical... Problem 29E: In a lottery game, a single ball is drawn at random from a container that contains 25 identical... Problem 30E: In a lottery game, a single ball is drawn at random from a container that contains 25 identical... Problem 31E: In a lottery game, a single ball is drawn at random from a container that contains 25 identical... Problem 32E: In a lottery game, a single ball is drawn at random from a container that contains 25 identical... Problem 33E: If the probability is .51 that a candidate wins the election, what is the probability that he loses? Problem 34E: If the probability is .03 that an automobile tire fails in less than 50,000 miles, what is the... Problem 35E: In Problems 35-38, use the equally likely sample space in Example 2 to compute the probability of... Problem 36E: In Problems 35-38, use the equally likely sample space in Example 2 to compute the probability of... Problem 37E: In Problems 35-38, use the equally likely sample space in Example 2 to compute the probability of... Problem 38E: In Problems 35-38, use the equally likely sample space in Example 2 to compute the probability of... Problem 39E: Given the following probabilities for an event E. find the odds for and against E : A38B14C.4D.55 Problem 40E: Given the following probabilities for an event E. find the odds for and against E : A35B17C.6D.35 Problem 41E: Compute the probability of event E if the odds in favor of E are A38B117C41D4951 Problem 42E: Compute the probabilities of event E if the odds in favor of E are A59B43C37D2377 Problem 43E: In Problems 43-48, discuss the validity of each statement. If the statement is always true, explain... Problem 44E: In Problems 43-48, discuss the validity of each statement. If the statement is always true, explain... Problem 45E: In Problems 43-48, discuss the validity of each statement. If the statement is always true, explain... Problem 46E: In Problems 43-48, discuss the validity of each statement. If the statement is always true, explain... Problem 47E: In Problems 43-48, discuss the validity of each statement. If the statement is always true, explain... Problem 48E: In Problems 43-48, discuss the validity of each statement. If the statement is always true, explain... Problem 49E: In Problems 49-52, compute the odds in favor of obtaining A head in a single toss of a coin Problem 50E: In Problems 49-52, compute the odds in favor of obtaining A number divisible by 3 in a single roll... Problem 51E: In Problems 49-52, compute the odds in favor of obtaining At least 1 head when a single coin is... Problem 52E: In Problems 49-52, compute the odds in favor of obtaining 1 head when a single coin is tossed twice Problem 53E: In Problems 53-56, compute the odds against obtaining A number greater than 4 in a single roll of a... Problem 54E: In Problems 53-56, compute the odds against obtaining 2 heads when a single coin is tossed twice Problem 55E: In Problems 53-56, compute the odds against obtaining A 3 or an even number in a single roll of a... Problem 56E: In Problems 53-56, compute the odds against obtaining An odd number or a number divisible by 3 in a... Problem 57E: (A) What are the odds for rolling a sum of 5 in a single roll of two fair dice? (B) If you bet $1... Problem 58E: (A) What are the odds for rolling a sum of 10 in a single roll of two fair dice? (B) If you bet $1... Problem 59E: A pair of dice are rolled 1,000 times with the following frequencies of outcomes: Use these... Problem 60E: A pair of dice are rolled 1,000 times with the following frequencies of outcomes: Use these... Problem 61E: In Problems 61-64, a single card is drawn from a standard 52-card deck. Calculate the probability of... Problem 62E: In Problems 61-64, a single card is drawn from a standard 52-card deck. Calculate the probability of... Problem 63E: In Problems 61-64, a single card is drawn from a standard 52-card deck. Calculate the probability of... Problem 64E: In Problems 61-64, a single card is drawn from a standard 52-card deck. Calculate the probability of... Problem 65E: What is the probability of getting at least 1 diamond in a 5-card hand dealt from a standard 52-card... Problem 66E: What is the probability of getting at least 1 black card in a 7-card hand dealt from a standard... Problem 67E: What is the probability that a number selected at random from the first 100 positive integers is... Problem 68E: What is the probability that a number selected at random from the first 60 positive integers is... Problem 69E: Explain how the three events A,B,andC from a sample space S are related to each other in order for... Problem 70E: Explain how the three events A,B,andC from a sample space S are related to each other in order for... Problem 71E: Show that the solution to the birthday problem in Example 5 can be written in the form PE=1P365n365n... Problem 73E: In a group of n people n12, what is the probability that at least 2 of them have the same birth... Problem 74E: In a group of n people n100, each person is asked to select a number between 1 and 100, write the... Problem 75E: If the odds in favor of an event E occurring are atob, show that PE=aa+b [Hint: Solve the equation... Problem 76E: If PE=c/d, show that odds in favor of E occurring are ctodc. Problem 77E: The command in Figure A was used on a graphing calculator to simulate 50 repetitions of rolling a... Problem 78E: Consider the command in Figure A and the associated statistical plot in Figure B. (A) Explain why... Problem 79E: Market research. From a survey involving 1,000 university students, a market research company found... Problem 80E: Market research. Refer to Problem 79. If a university student is selected at random, what is the... Problem 81E: Insurance. By examining the past driving records of city drivers, an insurance company has... Problem 82E: Insurance. Use the (empirical) probabilities in Problem 81 to find the probability that a city... Problem 83E: Quality control. A shipment of 60 game systems, including 9 that are defective, is sent to a retail... Problem 84E: Quality control. An assembly plant produces 40 outboard motors, including 7 that are defective. The... Problem 85E: Medicine. In order to test a new drug for adverse reactions, the drug was administered to 1,000 test... Problem 86E: Product testing. To test a new car, an automobile manufacturer wants to select 4 employees to... Problem 87E: Problems 87 and 88 refer to the data in the following table, obtained from a random survey of 1,000... Problem 88E: Problems 87 and 88 refer to the data in the following table, obtained from a random survey of 1,000... format_list_bulleted