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- Answers must be in 4 decimals 1. Bulsu plans to enforce speed limits using radar traps at 4 different locations within the campus. The radar traps at each of the locations L1, L2, L3, and L4 are operated 40%, 30%, 30%, and 20% of the time, and a person who is speeding on his way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations. If the person received a speeding ticket on his way to work, what is the probability that he passed through the radar trap located at L2? 2. A drug for the relief of asthma can be purchased from 5 different manufacturers in liquid, tablet, or capsule form, all of which come in regular and extra strength. How many different ways can a doctor prescribe the drug for a patient suffering from asthma?In an amusement arcade there is a horse race with horses coloured red, yellow and green. Only one player can play this game at any time and the outcomes of each race are independent of previous races. You can either bet 10p or 20p. If you bet 10p then each horse is equally likely to win. If you bet 20p the corresponding probabilities are 50%, 30% and 20%, respectively. Three times as many people bet 10p as do 20p. Given red wins, what is the probability it had been a 20p bet? 0.333 0.300 0.313 0.298Rock-Paper-Scissors is a simple game in which two players compete by simultaneously choosing rock, paper, or scissors. According to the classic rules of the game, paper beats rock, scissors beat paper, and rock beats scissors. After watching one player compete in this game for many rounds, you have observed that she chooses rock, paper, or scissors based on her previous choice according to the following transition probabilities: Future Choice Rock Paper Scissor Current Choice Rock 0.2 0.3 0.5 Paper 0.4 0.1 0.5 Scissor 0.7 0.3 0 Assume you are competing against this player and that you must decide on all future choices now (before seeing any additional opponent choices).a. What is the best strategy that works most of the time to beat your opponent? b. Given the opposing player last chose Rock, what is your best choice in the next round as her opponent ? c. Draw the transition diagram !
- Three cowboys Doc Holiday, Wyatt Erp, and Wild Bill are locked in a 3-way duel. When the churchbell rings at high noon, all three will draw their guns and fire one shot simultaneously. A hit is registered if a shooter is hit by either of the other two cowboys. Doc Holiday will randomly aim and fire at either Wyatt Erp or Wild Bill, with an even split probability of 0.5 of who he'll shoot at. Being a good shot, he has a 60% chance of hitting the target he fires at. Wyatt Erp will randomly aim and fire at either Doc Holiday or Wild Bill, with an even split probability of 0.5 of who he'll shoot at. Also a good shot, he has a 60% chance of hitting the target he fires at. Wild Bill will randomly aim and fire at either Wyatt Erp or Doc Holiday, with an even split probability of 0.5 of who he'll shoot at. Being a poor shot, he only has a 30% chance of hitting the target he fires at. Let X denote the number of cowboys that are hit after all three take one shot at the same time. a) What are…(QUEEN'S SECRET AND GENIES) In old days, there was a queen and she had a secret problem to solve. To get an answer to her secret problem, the queen bought one female and one male genie lamps. The probabilities that her secret problem can be solved by the male and female genies are 0.3 and 0.4 respectively. A Queen looking for divine help. Assume the queen keeps the genies independently away from each other with a fear that both could not harm her, what is the probability that the queen's secret problem is solved by at least one of the genies? Note: Please keep accuracy upto two decimal places.Your probability professor has a tabby cat who sleeps 34% of the time and seems to respond to stimuli more or less randomly. If a human pets her when she’s awake, she will request more petting 8% of the time, food 38% of the time, and a game of fetch the rest of the time. If a human pets her when she’s asleep, she will request more petting 33% of the time, food 41% of the time, and a game of fetch the rest of the time. (You can assume that the humans don’t pet her disproportionally often when she’s awake.) • If the cat requests food when petted, what is the probability that she was asleep? • If the cat requests a game of fetch when petted, what is the probability that she was not asleep?
- Please help!!! Q4. Ariana and Bella are playing a game. They each have 4 cards, which are numbered 1, 2, 3 and 4. Each shuffles her own cards and turns one over at random. If the cards show the same number, Ariana wins and Bella must pay Ariana $3. If the cards show different numbers, Bella wins and Ariana must pay Bella $1. By finding the probabilities of Ariana and Bella winning, show whether or not the game is fair.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.From a large survey of customers using a chain of coffee shops, 60% of the customers are male, 50% purchase food, 15% are both Male and purchase food. What are the probabilities that: A customer is both female and purchases food? A female customer purchases food? A customer purchasing food is female?
- A leisure ice rink in a recreational centre has public skate for 24 minutes, skating lessons for 27 minutes and ice cleaning for 9 minutes in every hour. When a person arrives at the leisure ice rink the probability the ice rink will be public skate or skating lessons is 3 20 11 20 C 250 17 20maya is playing a role playing game with her friends. She will roll a dice to determine if her character casts a spell. The odds in favor of her character casting a spell are 8/7. Find the probability of her character casting a spell.Police plan to enforce speed limits by using radar traps at four different locations within the city limits. The radar traps at each of the locations L1, L2, L3, and L4 will be operated 40%, 30%, 20%, and 30% of the time. If a person who is speeding on her way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations, what is the probability that she will receive a speeding ticket?
