You have an urn which contains one white and one black ball. At each second you pick a ball at random from the urn. You observe its color, return the ball into the urn, and add one more ball of the same color. What is the probability that if 15 balls are in the urn, all of them are black?
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- What if X doesn't have a value?There are four medals (Gold, Silver, Bronze and Wood) on a table, but they are all wrapped with dark wrapping paper, such that it is impossible to distinguish them. You would like to find the gold medal.The game starts as follows. You pick one medal without unwrapping it, and then the game host unwraps one of the remaining medals and reveals that it is a silver medal. (Assume here that the host unwraps a medal with equal probability, but knowing where the gold medal was and avoiding unwrapping the gold medal if still on the table, to keep the game interesting to watch until the end.)You have now three medals left to unwrap (one in your hand, two on the table). At this point, the host gives you the option to change your mind and swap your medal for one of the two left on the table. What would you do at this point? Would you keep your medal, or swap it with one of the two medals left on the table? If so, which one? Hints: Find the solution by using Bayes’ theorem, calculating all the…Consider a tournament between N teams, each team playing each of the other teams. Show (by example) there is a tournament that might occur, where every team is beaten by some team.
- Imagine there are N teams competing in a tournament, and that each team plays each of the other teams once. If a tournament were to take place, it should be demonstrated (using an example) that every team would lose to at least one other team in the tournament.A hallway has 100 locked lockers. A guy begins by opening each of the 100 lockers.He then shuts every other locker. Then, on his third pass, he toggles every third locker (closes if open, opens if closed). This method is repeated for 100 passes, such that the man toggles every ith locker on each pass i. How many lockers are open after his 100th journey along the corridor, in which he toggles just locker #100?A drawer contains 7 pair of socks where 8 socks are white, and 6 are red. In how many ways we can take 14 random socks out of the drawer so each sock is next to its matching pair. a. 441 ways b. 42 ways c. 1225 ways d. 70 ways
- One day, an elf jumps out at you from behind a garbage can and proposes a wager. He says that if the weather in Leipzig, Germany tomorrow is sunny, he'll give you $20, if it's cloudy (but dry) he'll give you $1, but if neither of those are the case you owe him $15. Helpfully, he also provides you data that indicates that the probability of sunny weather in Leipzig tomorrow is 40% and cloudy-but-dry is 10%. How much do you expect to win or lose from this wager (if you accept it)? A)Win $15.60 B)Lose $6.00C)Lose $7.50D)Win $0.60E)Win $4.00Implement Velocity Verlet • Bouncing test: Simulate two particles starting from some distance approaching each other with some speed. Plot x(t), v(t), V(t), K(t) and H(t). Are they bouncing? Is H conserved? • Find the longest ∆t that conserves H to high precision in the bouncing test . I want simulation in pythonA high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, theprincipal plays the following game: She asks the first student to open all the lockers. She then asks the secondstudent to close all the even-numbered lockers. The third student is asked to check every third locker. If it isopen, the student closes it; if it is closed, the student opens it. The fourth student is asked to check every fourthlocker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continuethis game. In general, the nth student checks every nth locker. If it is open, the student closes it; if it is closed,the student opens it. After all the students have taken turns, some of the lockers are open and some are closed.The program below, when ran, will prompt the user to enter the number of lockers in the school. After thegame is over, the program will output the number of lockers and the lockers numbers of the lockers…
- You have a mixed pile of N nuts and N bolts and need to quickly find the corresponding pairs of nuts and bolts. Each nut matches exactly one bolt, and each bolt matches exactly one nut. By fitting a nut and bolt together, you can see which is bigger, but it is not possible to directly compare two nuts or two bolts. Give an efficient method for solving the problem.Consider a game in which two players take turns removing any positive number of matches they want from one of two piles of matches. The player who removes the last match wins the game. Show that if the two piles contain the same number of matches initially, the second player can always guarantee a win.Suppose a person can buy a chocolate bar from the vending machine for $1 each. Inside every chocolate bar is a coupon. A person can redeem 3 coupons for one chocolate bar from the machine. This means that once a person has started buying chocolate bars from the machine, he/she always has some coupons. A person would like to know how many chocolate bars can be bought, if a person starts with N dollars and always redeem coupons, if he/she has enough for an additional chocolate bar. For example: With 3 dollars a person could buy 4 chocolate bars after purchasing 3 bars giving him/her 3 coupons and then redeeming the 3 coupons for one bar. This would leave him/her with one extra coupon. Thus, will have 4 chocolate bars and still have one coupon leftover. For 11 dollars, a person can have 16 chocolate bars and still have one coupon leftover. For 12 dollars, a person can have 17 chocolate bars and have two coupons leftover. Write a complete Python program that prompts a buyer to input…