Restaurants are notoriously difficult to make successful, often going out of business in the first three years. Many claim a key to success is good ratings from culinary critics in the first year of operation, but how important are they really? A sample of 1000 new restaurants found that 710 of them failed within three years. Of those that failed, 300 of them had good ratings from the critics in the first year, while for those that did not fail in the first three years, 200 of them had good first-year critics ratings. a) Your favorite restaurant has been running successfully for many years. Using the results given for the restaurant sample, estimate the chance that it had good first-year ratings. A new restaurant is being considered as it is thought that if it can stay in business for three years it will make a profit of $10,000. The question arises as to whether you should get a critic’s rating or not. Suppose that, given the restaurant survives, a good rating would increase the profits to $12,000. On the other hand, a bad rating would decrease profits to $5,000, given the restaurant survived. Do you think it is worth it to have the rating? Why or why not?