Concept explainers
In Exercises 15–20, decide whether the game is strictly determined. If it is, give the players’ optimal pure strategies and the value of the game. [HinT: See Example 4.]
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Finite Mathematics
- edo exercises 17 and 18 in section 8.1 of your textbook, about the small animal who lives in an area with woods and meadows, using the following data:If the animal is in the woods on one observation, then it is twice as likely to be in the woods as the meadows on the next observation. If the animal is in the meadows on one observation, then it is three times as likely to be in the meadows as the woods on the next observation.Assume that state 1 is being in the meadows and that state 2 is being in the woods.(1) Find the transition matrix for this Markov process. (2) If the animal is initially in the woods, what is the probability that it is in the woods on the next three observations? (3) If the animal is initially in the woods, what is the probability that it is in the meadow on the next three observations?arrow_forwardAssume that the group has a portfolio of 6 stocks. There is 30% chance that any one of these stocks will increase in value. Find the proability that four of the six stocks increase in value.arrow_forwardInternational Visitors The number of internationalvisitors to the United States for selected years 1986–2010 is given in the table below. If you had to pick one of these models to predictthe number of international visitors in the year2020, which model would be the more reasonablechoice?arrow_forward
- The casino game is played by a person called the shooter, who rolls two dice. There are two phases to the game. The first phase is called the 'come out' phase, and the second is called the 'point' phase. If the 'come out' roll of 2, 3, or 12, the shooter loses. If the 'come out' roll is a 7 or 11 , the shooter wins. Otherwise, the game progresses to the 'point' phase. Complete parts (a) through (c) below. (a) What is the probability that the players loses? (Type an integer or a simplified fraction.) (b) What is the probability that the player wins? (Type an integer or a simplified fraction.) (c) What is the probability that the player progresses to the 'point' phase? (Type an integer or a simplified fraction.)arrow_forwardExample 13.14. 800 candidates of both sexes appeared at an exmiantion. The boys outnumbered the girls by 15% of the total. The number of candidates who passed exceed the number failed by 480. Equal number of boys and girls failed in the examination. Prepare a 2 × 2 table and find the coefficient of association. Comment.arrow_forwardThe casino game is played by a person called the shooter, who rolls two dice. There are two phases to the game. The first phase is called the 'come out' phase, and the second is called the 'point' phase. If the 'come out' roll of 2, 3, or 12, the shooter loses. If the 'come out' roll is a 7 or 11, the shooter wins. Otherwise, the game progresses to the 'point' phase. Complete parts (a) through (c) below. (a) What is the probability that the player loses? The probability is nothing. (Type an integer or a simplified fraction.) (b) What is the probability that the player wins? The probability is nothing. (Type an integer or a simplified fraction.) (c) What is the probability that the player progresses to the 'point' phase? The probability is nothing. (Type an integer or a simplified fraction.)arrow_forward
- The casino game is played by a person called the shooter, who rolls two dice. There are two phases to the game. The first phase is called the 'come out' phase, and the second is called the 'point' phase. If the 'come out' roll of 2, 3, or 12, the shooter loses. If the 'come out' roll is a 7 or 11, the shooter wins. Otherwise, the game progresses to the 'point' phase. Complete parts (a) through (c) below. (a) What is the probability that the player loses?arrow_forwardFind the optimum strategy for player B. Choose the correct answer below and fill in the answer box(es) to complete your choice. OA. The game is strictly determined. Player B should choose column (Type a whole number.) OB. The game is not strictly determined. Player B should choose column 1 with probability, column 2 with probability ,and column 3 with probability (Type integers or simplified fractions.) The value of the game is (Type an integer or a simplified fraction.) # D L' 1. (10) Morearrow_forward2.)A jar contains 2 red, 3 green, and 6 blue marbles. In a game a player closes their eyes, reaches into the jar and randomly chooses two marbles. The player wins the game if at least one of their marbles is red. Suppose it costs $1 to play the game and the winning prize is $3. Mathematically analyze this game and determine if it is in your financial interest to play the game.arrow_forward
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