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 $6.00 C)Lose $7.50 D)Win $0.60 E)Win $4.00
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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 $6.00
C)Lose $7.50
D)Win $0.60
E)Win $4.00
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- The Monty Hall game is a statistical problem: there is a TV show (like the Monty Hall show) that allows contestants to choose between three doors, A, B, and C. Behind one of these doors is a new car (the winning door), and behind the other two are goats (the losing doors). After the contestant makes a choice, the game show host shows a goat behind one of the doors NOT chosen. The contestant is then given a choice to either switch to the other, non-opened door, or stick with their original guess. The interesting part of this “game" is the statistics involved –a person has a 1/3 chance of originally picking a winning door. The other door – that which is not revealed to have a goat but also was not originally chosen – actually has a 2/3 chance of being a winning door. Therefore, it is in the contestant's best interest to switch doors. You will create a program that simulates the Monty Hall game, where the computer plays the role of the host. The program must have no outputs, but 1) Ask…Jack and Jill will play a game called Hotter, Colder. Jill chooses a number from 0 to 100, and Jack makes repeated attempts to guess it. For each guess, Jill will respond with: hotter - if the current guess is closer to her number than the previous guess is colder - if the current guess is farther to her number than the previous guess is same - if the current guess is as far (to her number) as the previous guess is For Jack’s first guess, since there is no previous guess yet, Jill will just answer same. Describe an algorithm or a systematic approach that Jack can follow to win the games faster (fewer guesses). Example: Jill chooses number 40. Note: Jack can guess any number from 0 to 100 at any point of the game. Jack guesses 100. Jill responds same (first guess) Jack guesses 60. Jill responds hotter (60 is closer to 40 than previous guess 100) Jack guesses 80. Jill responds colder (80 is farther from 40 than previous guess 60) Jack guesses…The Monty Hall game is a statistical problem: there is a TV show (like the Monty Hall show) that allows contestants to choose between three doors, A, B, and C. Behind one of these doors is a new car (the winning door), and behind the other two are goats (the losing doors). After the contestant makes a choice, the game show host shows a goat behind one of the doors NOT chosen. The contestant is then given a choice to either switch to the other, non-opened door, or stick with their original guess. The interesting part of this “game" is the statistics involved-a person has a 1/3 chance of originally picking a winning door. The other door chosen – actually has a 2/3 chance of being a winning door. Therefore, it is in the contestant's best interest to switch doors. that which is not revealed to have a goat but also was not originally You will create a program that simulates the Monty Hall game, where the computer plays the role of the host. The program must have no outputs, but 1) Ask the…
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- EXERCISE - You go to a market to pick out some gourds to decorate your house for Halloween. The market has a special October deal where you get 3 randomly chosen gourdss for $10. Each gourd can either be an orange pumpkin, a green pumpkin or a squash. The probabilities for picking each one of them are: P(orange pumpkin) = 0.6, P(green pumpkin) = 0.3, and P(squash) = 0.1. A: What is the probability that the first gourd is an orange pumpkin, the second is a green pumpkin, and the third is a squash? B: What is the probability that you get all 3 as orange pumpkins? C: What is the probability that you get no squashes? D: What is the probability that you get at least one orange pumpkin? (ANSWERE USING PYTHON)Suppose we can buy a chocolate bar from the vending machine for $1 each.Inside every chocolate bar is a coupon. We can redeem six coupons for onechocolate bar from the machine. This means that once you have startedbuying chocolate bars from the machine, you always have some coupons.We would like to know how many chocolate bars can be eaten if we startwith N dollars and always redeem coupons if we have enough for an additional chocolate bar.For example, with 6 dollars we could consume 7 chocolate bars afterpurchasing 6 bars giving us 6 coupons and then redeeming the 6 couponsfor one bar. This would leave us with one extra coupon. For 11 dollars, wecould have consumed 13 chocolate bars and still have one coupon left.For 12 dollars, we could have consumed 14 chocolate bars and have twocoupons left.A coin is flipped 8 times in a row (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. Q1.1 What is the probability that it lands on heads exactly four times?
- You are given an instance of a problem where you have an n x n grid of squares. Each square can be unpainted or can have a hole, so you cannot go on the square with a hole. The objective is to paint all the squares that do not have a hole. You start in the square (0,0) which is unpainted. The actions you can do are: (1) paint the square you are on if it is not painted; (2) move, either vertically or horizontally, to an adjacent square inside the grid that is not painted and does not have a hole. a. Describe a state-space representation for the problem, specifying the state representation, the initial state, the goal condition, and the actions. b. Is the state space finite? Is it a tree or a graph? c. Propose a heuristic for the problem. Is your heuristics admissible or not? Explain briefly your answerSuppose 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…In a candy store, there are N different types of candies available and the prices of all the N different types of candies are provided to you. You are now provided with an attractive offer. You can buy a single candy from the store and get at most K other candies ( all are different types ) for free. Now you have to answer two questions. Firstly, you have to find what is the minimum amount of money you have to spend to buy all the N different candies. Secondly, you have to find what is the maximum amount of money you have to spend to buy all the N different candies. In both the cases you must utilize the offer i.e. you buy one candy and get K other candies for free. Example 1: Input: N = 4 K = 2 %3D candies[] = {3 2 1 4} Output: 3 7