The final match of world championship soccer is to be played between England and the Netherlands. The star player for the Dutch team, Dennis Nightmare, has been injured. The probability of his being fit enough to play in the final is being estimated at 75%. Pre-game predictions have estimated that, without Nightmare, the probability of a Dutch win is 30% and with Nightmare, 50%. Later, you hear that the Dutch team has won the match. Without having any other information about the events that occurred, what would you say was the probability that Dennis Nightmare played in the final?

The final match of world championship soccer is to be played between England and the Netherlands. The star player for the Dutch team, Dennis Nightmare, has been injured. The probability of his being fit enough to play in the final is being estimated at 75%. Pre-game predictions have estimated that, without Nightmare, the probability of a Dutch win is 30% and with Nightmare, 50%. Later, you hear that the Dutch team has won the match. Without having any other information about the events that occurred, what would you say was the probability that Dennis Nightmare played in the final?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

A psychologist is concerned about the health of veterans returning from war. She examines 36 veterans and assesses whether they show signs of post-traumatic stress disorder. What is the population of interest? All veterans with post-traumatic stress disorder All veterans returning from war The 36 veterans returning from war The veterans returning from war showing signs of post-traumatic stress disorder statistical power of 95% implies that it is very likely that H0 will be rejected if it is not true. the chance that the alternative hypothesis is true is 95%. the p-value for the study will be 5%. H0 is probably false.
if you have a problem where a percentage of male customers and and female customers purchase goods in a store. males comprise 60% of your customers and females 40% of customers. when a female enters the store, they make a puchace 35% of the time, but when a male enters he makes a purchase only 25% of the time. How would you determine the probability of an individual purchasing an item.
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?
There is an option of paying $100 to have research conducted to better predict which state of nature will occur. When the true state of nature is High, the research will accurately predict High 70% of the time. When the true state of nature is Low, the research will accurately predict Low 75% of the time. Given that the research is conducted, what is the joint probability that the state of nature is High and the research predicts Low?
The twins, Nikki and Sean want to open a small convenience store. They have to decide whether to build a small, medium or big store. They consulted their older brother, Dave, who is a market analyst. Dave told them that he just finished a market study for a similar venture and his findings indicated a 0.35 probability that demand will be low and a 0.65 probability that demand will be high. If Nikki and Sean build a small store and demand is low, the net present value will be $150,000. If demand is high they have the option to buy their inventory from a wholesaler and realize a net present value of $100,000. If they decide they want to expand, they stand to realize a net present value of $120,000. If the twins build a medium-sized store and demand is low, the net present value will be $175,000. If the demand turns out to be high, they can do nothing and realize a net present value of $100,000. If they expand, they could realize a net present value of $135,000. If Nikki and Sean build…
At a bar, 30% of those in attendance are football fans, 50% in attendance are soccer fans, and 20% in attendance are hockey fans. You may assume these sports fandoms are mutually exclusive. The probability that a football fan is wearing a red shirt is 15%. The probability that a soccer fan is wearing a red shirt is 45% and the probability that a hockey fan is wearing a red shirt is 85%. You have just talked to a randomly selected person who was wearing a red shirt, but forgot to ask them their preferred sport. What is the probability that they are a soccer fan? What is the probability that a randomly selected bar patron is a soccer fan AND they are wearing red? What is the probability that a randomly selected part goer is a soccer fan OR they are wearing red?
Milan
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
Suppose an oil company is thinking of buying some land for $10,000,000. There is a 60%60% chance of economic growth and a 40%40% chance of recession. The probability of discovering oil is 44%44% when there is economic growth and 32%32% when there is a recession. If there is economic growth and the oil company discovers oil, the value of the land will triple. If they do not discover oil, the value of the land will decrease by 10%.10%. If there is a recession and the company discovers oil, the value of the land will increase by 50%.50%. If they do not discover oil, the land will decrease in value by 75%.75%. What is the expected value of the investment? Give your answer to the nearest dollar. Avoid rounding within calculations. $$ Select the correct interpretation of the expected value. The expected value represents what the actual investment value will be for this land purchase of $10,000,000. The company should make the investment because the expected value…
You are analysing a factory. Stage 3 of the manufacturing process has a 45% chance of finishing on time. If it does finish on time, the chance of Stage 4 finishing late is 20%. The overall chance of Stage 4 finishing on time is 71.2%. What is the chance that Stage 4 finishes late if Stage 3 finished late? Round your answer to 2 decimal places.
If the probability that the Islanders will beat the Rangers in a game is 81%, what is the probability that the Islanders will win at least three out of five games in a series against the Rangers? Round your answer to the nearest thousandth.