A mouse is put into a T-maze. In this maze, he has the choice of turning to the left and beingrewarded with cheese or turning to the right and receiving a mild shock. Before any conditioningtakes place, the mouse is equally likely to go to the left or to the right. After the first trial, hisdecision is influenced by what happened on the previous trial. If he receives cheese on any trial,the probabilities of him going to the left or right become 0.9 and 0.1, respectively, on the followingtrial. If he receives the electric shock on any trial, the probabilities of him going to the left or righton the next trial become 0.65 and 0.35, respectively. What is the probability of the mouse turningright on the second trial?The probability of the mouse turning right on the second trial is(Type an integer or a decimal.)

To find the probability of the mouse turning right on the second trial, we can use conditional…

Answered: A mouse is put into a T-maze. In this…

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...

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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…
The Two-Way table below represents 2 bags of M&Ms. One bag id the peanut M&Ms and the other is the Milk Chocolate (without peanuts) M&Ms. Ms. Bradley pours both bags into a glass jar. Use the following Two-Way Table to answer the following prompts: Orange Red Yellow Green Blue Brown Milk Chocolate 13 15 18 19 16 14 Peanuts 9 11 8 7 12 10 What is the Probability of selecting a Orange Milk Chocolate and a blue Milk Chocolate M&M? After each selection the M&Ms are not placed back into the jar.
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.
Sally and Mike are playing frisbee at the beach. When Sally throws the frisbee the probability is 0.13 that it comes back to Sally, the probability is 0.7 that it goes to Mike, and the probability is 0.17 that the dog runs away with the frisbee. When Mike throws the frisbee there is a 0.62 probability that Sally gets it, a 0.27 probability that it comes back to Mike, and a 0.11 probability that the dog runs away with the frisbee. Treat this as a 3--state Markov Chain with the dog being an absorbing state. (a) If Mike has the frisbee, what is the expected value for the number of times the frisbee will be thrown before the dog gets the frisbee and runs away with it? (Give your answer correct to 2 decimal places.) times thrown (b) If Mike has the frisbee, what is the expected value for the number of times Mike will throw the frisbee before the dog gets it? (Give your answer correct to 2 decimal places.) times Mike throws
Joon wants to determine whether his San Jose oil field will yield oil. He has hired a geologist to run tests on the field. If there is oil in the field, there is a 95% chance that the test will indicate oil. If the field contains no oil, there is a 5% chance that the test will indicate oil. If the test indicates that there is no oil in the field, what is the probability that the field contains oil? Before the test, Joon believes that there is a 10% chance that the field will yield oil.
Suppose I flip a fair coin n = 20 times. A psychic tries to predict the outcome before each flip. Three researchers have different ideas about the psychic's ability. There is Sydney, the Skeptic (S), who thinks the psychic's success rate is between 49% and 51%. There is Morgan, the Mark, M, who thinks that the psychic's success rate is 80%. And there is Carter, the Cynic (C), who thinks the psychic's success rate is 10%. Specifically: S+ 0 ~ U(.49, .51) M + 0 = .80 C0 = .10 %3D In all cases, assume the number of successful predictions follows a binomial distribution with success rate 0. Usek for the number of successes and n for the number of trials. Given all that: Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Carter over Morgan. Call that Bayes factor Bc:M Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Morgan over Sydney. Call that Bayes factor BM:S Determine the formula for the Bayes factor (a.k.a., likelihood…
Wendy needs to get to an airport from a hotel. There is 0.33 chance that she calls a cab, there is 0.11 chance that she gets a Uber. If she cannot get a cab or Uber, she will take a shuttle. If she calls a cab, there is 0.29 chance that she could miss the flight. If she gets a Uber, the chance of missing flight is 0.22. If she takes the shuttle, the chance is 0.28. What is the probability that she misses the flight? (Round your answer to three decimal places)
You are hiking through the woods, and come across some tracks; based on your expe- rience, you estimate there is a 40% chance the tracks are from a dog, a 30% chance the tracks are from a wolf, a 20% chance the tracks are from a coyote, and a 10% chance the tracks are from some other animal. Your friend, also a nature lover, notices some white hairs in the tracks. They know that 20% of dogs have white hair, 50% of wolves have white hair, 10% of coyotes have white hair, and 30% of other animals in the area have white hair. What are the odds of these tracks coming from a dog, wolf, coyote, or other animal?
In a recent year, the percentage of patients at a doctor's office who received a flu shot was 60%. A campaign by the doctors and nurses was designed to increase the percentage of patients who obtain a flu shot. The doctors and nurses believed there was an 80% chance that someone who received a shot in year 1 would obtain a shot in year 2. They also believed that there was a 40% chance that a person who did not receive a shot in year 1 would receive a shot in year 2. Complete parts (a) through (c) below. (a) Give the transition matrix for this situation. Set up the transition matrix P so that the first row and first column represent obtaining a flu shot and the second row and second column represent not obtaining a flu shot. P = (Type an integer or decimal for each matrix element.)
Two machines turn out all the paper bags produced in the plant. Machine A produces 38% of the bags and machine B produces 62% of the bags. Machine A produces defective bags 1.9% of the time and machine B produces defective bags 3.8% of the time. Given a defective bag, what is the probability that it came from machine B?
Global Airlines operates two types of jet planes: jumbo and ordinary. Of Global's air fleet, 40% of its capacity is provided on jumbo jets. Global serves two types of customers, business and tourist. Business customers are 70% of Global customers, while tourists make up 30%. 15% of Global's customers fly on jumbo jets and are tourists. What is the probability that a customer is a tourist and flies on a regular jet?
In a certain community, eight percent of all adults over age 50 have diabetes. If a health service in this community correctly diagnosis 95% of all persons with diabetes as having the disease and incorrectly diagnoses ten percent of all persons without diabetes as having the disease, find the probabilities that: The health service will diagnose an adult over age 50 as having diabetes. A person over 50 diagnosed by the health service as having diabetes actually has the disease.

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