In the hiring problem, what is the probability that the n’th best candidate will be hired after being interviewed
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In the hiring problem, what is the probability that the n’th best candidate will be hired after being interviewed?
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- A standard deck of playing cards consists of 52 cards. Each card has a rank and a suit. There are 13 possible ranks (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K), 4 possible suits (spades, clubs, hearts, diamonds), and 13 cards in each suit (one of each rank). A hand of 9 cards is drawn from a standard deck of 52 cards (assume all outcomes are equally likely). For each of the following questions, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4, 2)/24) instead of 0.375.What is the probability of getting at least 5 heads in 6 tosses of a fair coin?A group of 15 students made up of 9 females and 6 males form a committee of 5. What is the probability the committee is all male?
- Q3/ For a given exam, there is 40% of the students passed math test, and 30% passed biology test, and 20% passed both math and biology tests. What is the probability that a randomly selected student failed biology given that he passed math? (Use Venn diagram)A group of 15 students made up of 9 females and 6 males form a committee of 5 What is the probability the committee is made up of 3 females and 2 males?In a party, there are 10people with white shirts and 8 people with red shirts; 4 people have black shoes and white shirts; 3 people have black shoes and red shirts; The total number of people with white or red shirts or black shoes is 21. How many people have black shoes?
- In a pizza topping preference poll, people voted for their favorite toppings as follows: Topping Votes Mushrooms 8 Cheese 27 Pepperoni 36 Sausage 16 Bacon 23 Construct a Pareto chart for the data. What is the relative frequency for the preference of sausage? 52.2% 27% 14.5% 16% 57.6%A student goes to the school canteen. The probability that they get fish is 0.2, get chips is 0.5, or both is 0.1. What is the probability that the student gets fish, chips, OR both?During the internship season m tech companies are looking to hire CS undergrads, each company has k number of available positions. There are also n CS undergrads, each interested in joining one of the companies. After all the interviews each company has rankings of students in order of preference, and each student has a ranking of companies in order of preference. We can assume that there are more internship slots available than the number of students. (This means that at the end not all slots will be filled.) Describe an algorithm that finds a stable assignment of students to companies. That is, each student will get assigned to one company and the resulting matching is stable. In your answer make sure to follow the guidelines of solving an algorithmic problem, as described above.
- Hat-check problem. Use indicator random variables to solve the following problem, which is known as the hat-check problem. Each of n customers gives a hat to a hat-check person at a restaurant. The hat-check person gives the hats back to the customers in a random order. What is the expected number of customers who get back their own hat?4. The probability that a driver must stop at any one traffic light coming to IUKL is 0.2. What is the probability that a student must stop at the traffic light at most 2 out of 9 sets of traffic lights?If the company invests 100,000 USD or less, their profit will be based on 75,000 USD as first 25,000 USD goes to set up the business in the first place. For the first 100,000 USD, the profit margin is low: 4.5%. Therefore, for every 100 dollar they spend, they get a profit of 4.5 dollar. For an investment greater than 100,000 USD, for the first 100,000 USD (actually on 75,000 USD as 25,000 is the setup cost), the profit margin is 4.5% whereas for the rest, it goes up to 8%. For example, if they invest 250,000 USD, they will get an 8% profit for the 150,000 USD. In addition, from the rest 100,000 USD, 25,000 is the setup cost and there will be a 4.5% profit on the rest 75,000. The investment will always be greater or equal to 25,000 and multiple of 100. Complete the RECURSIVE methods below that take an array of integers (investments) and an iterator (always sets to ZERO(‘0’) when the method is initially called) and prints the profit for the corresponding investment. You must…