Suppose you have two boxes A and B. Box A contains 7 black marbles, 4 white marbles. Box B contains 7 white and 4 black marbles. A random experiment is performed in two sequential trials by first drawing a marble randomly from box A and putting into Box B. In the second trial after the first trial, a marble is drawn randomly from box B. If we reverse the scenario, then what is the probability of drawing a black marble from box A given that a white marble is drawn from box B.
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Suppose you have two boxes A and B. Box A contains 7 black marbles, 4 white marbles. Box B contains 7 white and 4 black marbles. A random experiment is performed in two sequential trials by first drawing a marble randomly from box A and putting into Box B. In the second trial after the first trial, a marble is drawn randomly from box B.
- If we reverse the scenario, then what is the probability of drawing a black marble from
box A given that a white marble is drawn from box B.
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- Consider the following scenario:A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, the principal plays the following game: She asks the first student to open all the lockers. She then asks the second student to close all the even-numbered lockers. The third student is asked to check every third locker. If it is open, the student closes it; if it is closed, thestudent opens it. The fourth student is asked to check every fourth locker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continue this 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 see in the photo, when ran, should ask the user to enter the number of lockers in the school. The program will output the number of lockers and the…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?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…
- 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…A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, the principal plays the following game: She asks the first student to open all the lockers. She then asks the second student to close all the even-numbered lockers. The third student is asked to check every third locker. If it is open, the student closes it; if it is closed, the student opens it. The fourth student is asked to check every fourth locker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continue this 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 the game is over, the program will output the number of lockers and the lockers numbers of the…A test with 20 questions was applied to 300 people. We know that 8 questions had at least 100 right answers and the rest at least 200 right answes. Prove by contradiction that some student got at least 11 questions right.
- Consider the following scenario: A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, the principal plays the following game: She asks the first student to open all the lockers. She then asks the second student to close all the even-numbered lockers. The third student is asked to check every third locker. If it is open, the student closes it; if it is closed, the student opens it. The fourth student is asked to check every fourth locker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continue this 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 the game is over, the program will output the number of…Mastermind is a code-breaking game for two players. In the original real-world game, one player A selects 4 pegs out of 6 colors and puts them in a certain fixed order; multiples of colors are possible (for example, red-green red-green). His opponent B does not know the colors or order but has to find out the secret code. To do so, B makes a series of guesses, each evaluated by the first player. A guess consists of an ordered set of colors which B believes is the code. The first player A evaluates the guess and feeds back to B how many positions and colors are correct. A position is correct ("black") if the guess and the secret code have the same color. Additional colors are correct ("white"), if they are in the guess and the code, but not at the same location. For example1 2 3 4secret: red-green red greenguess: red blue green purpleresults in one correct position ("black = 1") for the red peg at position one and one additional correct color ("white=1") for the green peg in the guess.…Mastermind is a code-breaking game for two players. In the original real-world game, one player A selects 4 pegs out of 6 colors and puts them in a certain fixed order; multiples of colors are possible (for example, red-green red-green). His opponent B does not know the colors or order but has to find out the secret code. To do so, B makes a series of guesses, each evaluated by the first player. A guess consists of an ordered set of colors which B believes is the code. The first player A evaluates the guess and feeds back to B how many positions and colors are correct. A position is correct ("black") if the guess and the secret code have the same color. Additional colors are correct ("white"), if they are in the guess and the code, but not at the same location. For example1 2 3 4secret: red-green red greenguess: red blue green purpleresults in one correct position ("black = 1") for the red peg at position one and one additional correct color ("white=1") for the green peg in the guess.…
- Problem 1. You are playing a version of the roulette game, where the pockets are from 0 to 10and even numbers are red and odd numbers are black (0 is green). You spin 3 times and add up the values you see. What is the probability th at you get a total of 17 given on the first spin you spin a 2? What about a 3? Solve by simulation and analytically.There are 4 balls in a jar (2 black and 2 white). You randomly choose three balls (one by one with no replacement) and paint them according to one of the following methods (a-c) and replace them in the jar. You ask your friend to pick a ball. What is the probability that this ball is white? a. You paint them all black. b. You paint them all the same color as the first ball that is picked c. You look at the majority color (among the 3 selected ones) and paint them all that color. Write a MATLAB code to simulate each of the above 3 cases in MATLAB for 10,000 times and estimate the probability of getting a white ball in each of those casesSuppose you are a participant in a game show. You have a chance to win a motorbike. You are askedto select one of the 500 doors to open; the motorbike is behind one of the 500 doors; the other remaining doorsare losers and have balloons behind them. Once you select a door, the host of the game show, who knowsexactly what is behind each of the door, randomly opens 480 of the other doors all at once that s/he for sureknows are losing doors and have balloons behind them. Then s/he reoffers you – whether you would like toswitch to the other doors or keep your initial or original selection as before. Now in this case, you are goingto make decision based on probabilistic reasoning. Therefore, whenever you are reoffered by the host to dothe selections among the remaining unopened doors, what is the probability of winning for each of theremaining unopened doors (including your original selection)? Do you want to make a switch based on theprobabilistic reasoning? If you are switching, which…