The star quarterback of a university football team has decided to return for one more season. He tells one person, who in turn tells someone else, and so on, with each person talking to someone who has not heard the news. At each step in this chain, if the message heard is "yes" (he is returning) then there is a 5% chance it will be changed to "no," and if the message heard is "no," then there is a 15% chance that it will be changed to "yes." Determine the probability that the fourth person in the chain hears the correct news. (A graphing calculator is recommended. Assume that the quarterback is not part of the chain. Round your answer to one decimal place.)

The star quarterback of a university football team has decided to return for one more season. He tells one person, who in turn tells someone else, and so on, with each person talking to someone who has not heard the news. At each step in this chain, if the message heard is "yes" (he is returning) then there is a 5% chance it will be changed to "no," and if the message heard is "no," then there is a 15% chance that it will be changed to "yes." Determine the probability that the fourth person in the chain hears the correct news. (A graphing calculator is recommended. Assume that the quarterback is not part of the chain. Round your answer to one decimal place.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Suppose that 11% of people are left-handed. If 5 people are selected at random, find the probability that exactly 2 are left- handed. For problem #5, find the probability that 2 or less are lefthanded.
The gunner on the assault boat SS Minnie Chang fires six missiles at an attacking plane. Each has a 20% chance of being on target. If two or more shells find their mark, the plane will crash. At the same time, the pilot of the plane fires 10 surface-to-air rockets, each of which has a 0.05 chance of sinking the boat. If you want to live, would you rather be on the plane or on the boat?
In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 6% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is an 8% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.) (a) in 1 month nonsmokers people 1 pack/day or less people more than 1 pack/day people (b) in 2 months nonsmokers people 1 pack/day or less people more than 1 pack/day…
An electronics store expects to have ten returns per day on average. The manager wants to know the probability of the store getting fewer than eight returns on any given day.
In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 7% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month?
A man buys a racehorse for $25,000 and enters it in two races. He plans to sell the horse afterward, hoping to make a profit. If the horse wins both races, its value will jump to $105,000. If it wins one of the races, it will be worth $65,000. If it loses both races, it will be worth only $10,000. The man believes there is a 30% chance that the horse will win the first race and a 35% chance that it will win the second one. Assuming that the two races are independent events, find the man's expected profit.
Milan
You are an analyst for a consumer products company. You run a survey of 1000 customers and find that 80% of customers use gel packs for laundry detergent (the rest use liquid or powder) and 40% of customers use gel packs for their dishwasher detergent (the rest use liquid or powder). You also learn that twice as many customers use laundry detergent than dishwasher detergent.
You are an analyst for a consumer products company. You run a survey of 1000 customers and find that 80% of customers use gel packs for laundry detergent (the rest use liquid or powder) and 40% of customers use gel packs for their dishwasher detergent (the rest use liquid or powder). You also learn that twice as many customers use laundry detergent than dishwasher detergent.
In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 9% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.)(a) in 1 month:nonsmokers:1 pack/day or less:more than 1 pack/day:(b) in 2 months:nonsmokers:1 pack/day or less:more than 1 pack/day:(c) in 1 year:nonsmokers:1 pack/day or less:more than 1 pack/day:
The weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 40% chance it will be good tomorrow, a 30% chance it will be indifferent, and a 30% chance it will be bad. If the weather is indifferent today, there is a 50% chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 10% chance it will be good tomorrow and a 30% chance it will be indifferent. a. What is the stochastic matrix, P, for this situation? b. Suppose there is a 10% chance of good weather today and a 90% chance of indifferent weather. What are the chances of bad weather tomorrow? c. Suppose the predicted weather for Monday is 40% indifferent weather and 60% bad weather. What are the chances for good weather on Wednesday? a. Create the stochastic matrix, P, where G is good, I is indifferent, and B is Bad. From: GIB a (Simplify your answers.) To: G
June is a student taking a statistics course. Unfortunately, June is not a diligent student. She does not read the textbook before or after class, does not do homework, and regularly misses class. She intends to rely on luck to pass the next quiz. The quiz consists of 10 multiple-choice question. Each question has five possible answers. Only one of the answers is correct, so the probability of choosing the correct answer is 0.20. June plans to guess the answer to each question independently. Let � be the number of correct answers on June’s quiz. What is the standard deviation of correct answers for June? Group of answer choices 8 2 1.26 1.14 None of These