Two people are playing tic-tac-toe. How many ways can they make the first two moves, if we only count board positions that are different under any symmetry of the board?
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Two people are playing tic-tac-toe. How many ways can
they make the first two moves, if we only count board positions that
are different under any symmetry of the board?
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- Hi, please help me with this question and please be specific with your solution Thanks a lotA bag of coins contains nine pennies, six nickels, four dimes, and three quarters. Assuming that the coins of any one denomination are identical, in how many ways can 10 coins be selected? The answer is C(13,3) - C(3,3) - C(6,3) - C(8,3) - C(9,3) + C(4,3) I just have no idea where to start. Thanks!The game Capture is played by two players, First and Second, who take turns to move towards one another on a narrow bridge. Initially, the two players are at opposite ends of the bridge, at a distance of n feet from each other. (Here n is an arbitrary positive integer.) When it is their turn, they are allowed to jump 1, 2, or 3 feet toward each other. The game starts by First making a move first; the game is over when one player is able to capture (jump on top of) the other player. Generalize the problem further to the case when the initial distance is n feetand the players are allowed to jump any (positive) integer number of feet up to k feet. (Here n and k are arbitrary natural numbers.)
- Makalya is playing a game using a wheel divided into eight equal sections, as shown in the diagram below. Each time the spinner lands on brown or orange, she will win a prize. Simplify your answer. Brown White Green Orange Yellow Brown Brown White P (brown or orange) = [Select ] %3D P (brown first then orange) = [ Select ] %3D DELLA game known to most children is rock-paper-scissors. On the count of three, each person displays rock (fist), paper (palm), or scissors (two fingers extended). Rock beats scissors, scissors beats paper, and paper beats rock. Let's say three people play according to these rules. If all three match, player 1 wins, if all three are different, player 2 wins; otherwise, player 3 wins. Is this a fair game? Why or why not? If it is not a fair game, modify the game so that it becomes fair.Q3
- To raise money for the local Veterans Affairs hospital, your friend organizes a fundraiser, inviting you to play a two-stage game where you pay $6 to play. The game works as follows: a fair 8-sided die is rolled, noting the number shown, and a spinner divided into 4 equal regions of different colors (blue, red, green, orange) is spun, noting th color. If the die shows 3 or the spinner shows orange, then you win $21. If the die shows an even number and the spinner does not show orange, then you win $7. Otherwise, you do not win anything. Let X be your net winnings. (a) Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact. P(X) Enter a fraction, integer, or exact decimal. Do not approximate (b) Compute your expected net winnings for the game. Round your answer to the nearest cent. (c) Is this game fair? O Yes O NoTraditionally, the game of Rock, Paper, Scissors is played with two people. Each of the two people, on the count of 3, reveals their hand in the shape of a rock, a piece of paper, or a pair of scissors as best they can (usually with a closed fist, a flat hand, or their index and middle fingers outstretched to form the V of an open pair of scissors). As the rules go, rock smashes scissors, paper covers rock, and scissors cuts paper. The game can be extended to an arbitrarily large number of, say, nn people, where nn is greater than or equal to 2. If when all nn people reveal their play and only 1 or all 3 options appear, that round is deemed indecisiveindecisive and they just play again. If when all nn people reveal their play precisely two of the three options appear, that round is decisivedecisive, and those with the winning play continue while those with the losing play are eliminated. Play continues until only one person remains. Assume the game begins with nn players, each of whom…please do the last question(Q3) as well Define a game as follow: you begin with an urn that contains a mixture of black and white balls, and during the game you have access to as many extra black and white balls as you need. In each move of the game, you remove two balls from the urn without being able to see what colour they are. Then you look at their colour and do the following: If the balls are the same colour, you keep them out of the urn and put a black ball in the urn. if the balls are different colours, you keep the black one out of the urn and put the white one back into the urn. Each move reduces the number of balls by one, and the game will end when only one ball is left in the urn. In this you will figure out how to predict the colour of the last ball in the urn and prove your answer using mathematical induction. Q1) Draw diagrams to map out all the possibilities for playing the game starting with two balls in the urn, then three balls, then four balls. For each case…
- two players A and B agree to play until one of them wins a certain number of games. P(A wins a game)=p and P(B wins a game)=1-p=q. However, they are forced to quit when A still has a games to win and B still has b games to win. How should they divide their stance to be fair?Packages arrive at the stockroom and are delivered on carts to offices and laboratories by student employees. The carts and packages are various sizes and shapes. The students are paid according to the carts used. There are 6 carts and the pay for their use is Product C1: $1 Product C2: $3 Product C3: $2 Product C4: $4 Product C5: $1 Product C6: $2 On a particular day, 9 packages arrive, and they can be delivered using the 6 carts as follows: C1 can be used for packages P1, P3, P4 and p7. C2 can be used for packages P2, P5, and P6, and p8. C3 can be used for packages P1, P2, P5, P6, and P7. C4 can be used for packages P3, P6, and P7 and 9. C5 can be used for packages P2, P4 and p8. C6 can be used for packages P1, P2 and P3 The stockroom manager wants the packages delivered at minimum cost. Using minimization techniques described in this unit, present a systematic procedure for finding the minimum cost solution. Use Petrik MethodCatalina participates in a game that consists of spinning a roulette with 6 segments of the same size numbered from 1 to 6. The roulette randomly stops at a numbered segment.This is the game: Catalina spins the wheel only once. She wins $ 1 if the wheel stops at number 1, $ 3 if the wheel stops at number 2, $ 5 if the wheel stops at number 3, and $ 7 if the wheel stops at number 4. She loses $ 1.25 if roulette stops at 5 or 6. (a) Calculate the expected value of participating in the game.____ pesos b) What can Catalina expect in the long run after playing several times?1) Catalina can expect to earn money.She can expect to earn ___ pesos per spin of the roulette wheel. 2) Catalina can expect to lose money.She can expect to lose ___ pesos per spin of the roulette wheel. 3) Catalina can expect to draw (she neither wins nor loses money)