In a game, two coins are tossed. If either of the coins comes up heads, you have won a prize. To claim the prize, you must point to one of your coins that is a head and say 'look, that coin's a head, I've won'. You watch Fred play the game. He tosses the two coins, and he points to a coin and says 'look, that coin's a head, I've won'. What is the probability that the other coin is a head?
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- 20 students from economics department were asked about their favourite course. 7 students said statistics, 3 of them said game theory, 9 of them said Microeconomics, 1 student said finance and 0 student said mathematics for economists. Draw a bar chart to represent the above information.(I have briefly shown you a bar chart during lecture. It’s nothing difficult but if you have any confusion, refer to the book or email me)A movie production company is releasing a movie with the hopes that many viewers will return to see the movie in the theater for a second time. Their target is to have 30 million viewers, and they want more than 30% of the viewers to want to see the movie again. They show the movie to a test audience of 175 people, and after the movie they asked them if they would see the movie in theaters again. Of the test audience, 65 people said they would see the movie again. a. Specify the competing hypotheses to test if more than 30% of the viewers will return to see the movie again. Ho: 0.3; versus HA b-1. Calculate the value of the test statistic. Note: Round final answer to 2 decimal places. Test statistic b-2. Find the p-value. O 0.025 s p-value < 0.05 O 0.05 s p-value < 0.10 O p-value ≥ 0.10 O p-value < 0.01 O 0.01 s p-value < 0.025 c. At the 5% significance level, what is the conclusion? ○ Do not reject Ho, the population proportion is greater than 0.30. ○ Do not reject Ho, the population…Three players enter a room and are given a red or a blue hat to wear. The color of each hat is determined by a fair coin toss. Players cannot see the color of their own hats, but do see the color of the other two players' hats. The game is won when at least one of the players correctly guesses the color of his own hat and no player gives an incorrect answer. In addition to having the opportunity to guess a color, players may also pass. Communication of any kind between players is not permissible after they have been given hats; however, they may agree on a group strategy beforehand. The players decided upon the following strategy. A player who sees that the other two players wear a hat with the same color guesses the opposite color for his/her own hat; otherwise, the player says nothing. What is the probability of winning the game under this strategy?
- At a county fair, you pay $2 to play the following game: You are given a fair coin, and two bags standin front of you, labelled Bag A and Bag B. You flip a coin: If your coin lands Heads, you pick a ballfrom Bag A. If your coin lands tails, you pick a ball from Bag B. Each ball has a dollar value written onit, and you win the number of dollars shown on the ball. • Bag A contains four (4) balls in total: Three (3) balls show $1, and one (1) ball shows $5.• Bag B contains three (3) balls in total: Two (2) balls show $2, and one (1) ball shows $3.You WIN money if you leave with more money than you started with. You LOSE money if you leavewith less money than you started with. You BREAK EVEN if you leave with the same money that youstarted with.Let H denote the event that you flip heads, T denote the event that you flip tails, W the event that youwin, and L the event that you lose.(i) You pay to play exactly one game. What is the probability that you WIN given thatyou flipped a Heads?(ii)…You are given the chance to play one of two games: One where there is a 20% chance of you winning 8 dollars and an 80% chance of winning 128 dollars. For the second game you have a 20% chance of winning two dollars and an 80% chance of winning 256 dollars. Which lottery is worth more on average, and how much is it worth discrete mathZara and Sue play the following game. Each of them roll a fair six-sided die once. If Sue’s number is greater than or equal to Zara’s number, she wins the game. But if Sue rolled a number smaller than Zara’s number, then Zara rolls the die again. If Zara’s second roll gives a number that is less than or equal to Sue’s number, the game ends with a draw. If Zara’s second roll gives a number larger than Sue’s number, Zara wins the game. Find the probability that Zara wins the game and the probability that Sue wins the game. Note: Sue only rolls a die once. The second roll, if the game goes up to that point, is made only by Zara.
- Directions: Create two (2) problems illustrating a permutation situation. Be creative in your problem by citing some of your personal interests. Determine the number of outcomes in your created permutation problem.You have been asked to play a card game. A card is dealt from a complete deck offifty-two cards (no jokers). A deck has 4 aces, 4 kings, 4 queens, 4 jacks, and 36 other cards.It works like this:• If the card is a ace, you lose $4.• If the card is a king or jack, you lose $10.• If the card is a queen, you win $8.• If the card is anything else, you win $1.Find the expected value of the game. Write the excepted value rounded to the nearest centYou are a contestant on a game show. There are three closed doors in front of you. The game show host tells you that behind one of these doors is a million dollars in cash, and that behind the other two doors there are trashes. You do not know which doors contain which prizes, but the game show host does. The game you are going to play is very simple: you pick one of the three doors and win the prize behind it. After you have made your selection, the game show host opens one of the two doors that you did not choose and reveals trash. At this point, you are given the option to either stick with your original door or switch your choice to the only remaining closed door. To maximize your chance to win a million dollars in cash, should you switch? Choices: A) Yes B) No C) It doesn't matter because the probability for you to win a million dollars in cash stays the same no matter if you switch or not.