Consider the game "Battle of the Sexes" as below. In the mixed-strategy equilibrium, Roger chooses to watch a movie with the probability y* of: Roger 0.5 1/4 3/4 1/3 Watch soccer Watch a movie Michelle Watch soccer 3,1 0,0 Watch a movie 0,0 1,3
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- (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.Question 11: Find the probability that at least one of them gets off on the 5th floor. O .271 O .3 O .336Q6
- 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?Roulette: You bet on numbers 1-18. What's the likelihood of winning after one trial? Explain your answer.Becky and Carla take an advanced yoga class. Becky can hold 29% of her poses for over a minute, while Carla can hold 35% of her poses for over a minute. Suppose each yoga student is asked to hold 50 poses. Let B the proportion of poses Becky can hold for over a minute and C = the proportion of poses Carla can hold for over a minute. What is the probability that Becky's proportion of poses held for over a minute is greater than Carla's? Find the z-table here. O 0.159 O 0,259 0 0.448 O 0,741 Save and Exit Next Submit Math and rem 96 & 7 8 9. 10
- 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…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.
- An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option willbe worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20and 30, the option will be worth $200. A trader thinks there is a 50% chance that the stock will closein the 20-30 range, a 20% chance that it will close above 30, and a 30% chance that it will fall below20. a) Create a valid probability table.b) How much should the trader expect to gain or lose?c) Should the trader buy the stock? Why?At the close of the stock markets on a day in 2013, there were 5905 companies listed with a certain stock exchange. On this day, the probabilities of advancing, declining, and unchanged company stocks appears in the table for the two exchanges. Find the probability an unchanged stock was listed on Exchange 1. Exchange Exchange 1 Exchange 2 Percentage of Probability of Probability of Stock Stock Companies Listed Advancing Declining 0.045 0.267 0.047 0.297 54.4% 45.6% The probability that an unchanged stock was listed on Exchange 1 is (Round to three decimal places as needed.) Probability the Stocks Remain Unchanged 0.045 0.047After a workday, you visit a bar from monday to friday. The bar offers four differrent beer flavors. Each day you select one flavor with the following probabilities: flavor 1 with 30% flavor 2 with 25% flavor 3 with 40% flavor 4 with a 5% What is the probability that the first time you eat flavor 3 is on tuesday?
