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- Suppose 55 percent of the customers at Pizza Palooza order a square pizza, 78 percent order a soft drink, and 43 percent order both a square pizza and a soft drink. Is ordering a soft drink independent of ordering a square pizza? Yes NoA particular two-player game starts with a pile of diamonds and a pile of rubies. Onyour turn, you can take any number of diamonds, or any number of rubies, or an equalnumber of each. You must take at least one gem on each of your turns. Whoever takesthe last gem wins the game. For example, in a game that starts with 5 diamonds and10 rubies, a game could look like: you take 2 diamonds, then your opponent takes 7rubies, then you take 3 diamonds and 3 rubies to win the game.You get to choose the starting number of diamonds and rubies, and whether you gofirst or second. Find all starting configurations (including who goes first) with 8 gemswhere you are guaranteed to win. If you have to let your opponent go first, what arethe starting configurations of gems where you are guaranteed to win? If you can’t findall such configurations, describe the ones you do find and any patterns you see.Suppose 60 percent of the customers at Pizza Palooza order a square pizza, 80 percent order a soft drink, and 48 percent order both a square pizza and a soft drink. Is ordering a soft drink independent of ordering a square pizza?
- Suppose 40 percent of the customers at Pizza Palooza order a square pizza, 80 percent order a soft drink, and 32 percent order both a square pizza and a soft drink. Is ordering a soft drink independent of ordering a square pizza? multiple choice No YesA Company has 800 employees who bank with the Bank of Berba and First Public Bank. 312 bank with the Bank of Berba and 564 bank with the First Public Bank.How many employees bank with both banks, if 12 employees have no bank accounts?Suppose for your afternoon snacks, you may select juice, milk tea, or soda for yourdrinks. You also have three choices for your sandwich, ham, tuna, or cheese. How manypossible snacks are there?
- During intramurals the sports coordinator finds that, of its 175 students, 96 plays basketball, 86 plays volleyball and 60 plays sepak takraw. Also 33 plays basketball and volleyball, 27 plays basketball and sepak takraw, 32 plays volleyball and sepak takraw, and 15 plays the three games. How many students did not play in any of the three games?Suppose in two local counties, the locals have toad collecting contests. In the two largest,the average number of toads collected by contestants is µ1 = 43 with σ1 = 11 and µ2 = 55(Obviously a county with a larger toad population) with σ2 = 15. Cindy entered into contestnumber one and collected 56 toads and her sister Mindy entered into contest number two andcollected 73 toads. Which sister did better in the contest?In the 4th volume of the light novel KonoSuba, Kazuma, Aqua, Megumin, Darkness, and Wiz are bound to travel on Arcanletia. They have picked a carriage that can accommodate five persons; however, for some reason, the carriage can only accommodate four persons at that day. This indicates that one should sit on the carriage’s floor along with their bags. To settle who will sit on the floor, Kazuma and Aqua decided to play three rounds of Rock-Paper-Scissors. Aqua wins if she won at least one of the rounds, and Kazuma wins if he won all of the rounds. Determine the following: (a) Probability of Aqua winning. (b) Probability of Kazuma winning.
- Buu has 6 different types (named 1 to 6) of chocolates (in large quantity). Now he plays a game to eat those chocolates. He throws a die (of six sides, non-biased, if the die shows 1, he eats chocolate 1. If the die shows 2, he eats chocolate 2 and so on. Now let X be the number of chocolates of type 1 are eaten and Y be the number of chocolates of type 2 are eaten. What is joint PMF of X and Y ?(Total number of times he roll the die is 4.)At the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that z − u = 3(x − y) + 22 x + y = 50 + z + u and x − y + z − u = 58. How large was the audience of each of the four companies at the end of that year? Microsoft Time Warner Yahoo GoogleHow many ways can a photographer arrange 10 friends in a row for a photo if two of the friends are currently not in good terms and refuses to be beside each other?