The injured football player Bad news everyone! There is 1 second left in the game, and Tom Brady has injured himself. The matrices below depict the relative probabilities of winning givenan offensive and a defensive play call. (The row player is the New England Patriots and the column player is the opponent.) How much has the all star's home team probability of winning decreased due to the injury? Patriots Opponent
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- The project manager of Good Public Relations gatheredthe data shown in Table 7.15 for a new advertisingcampaign.a. How long is the project likely to take? b. What is the probability that the project will take more than38 weeks?c. Consider the path A–E–G–H–J. What is the probability thatthis path will exceed 38 weeks?According to the Intern al Revenue Service, the mean tax refund for the year 2014 was $2800 Assu me the stan dard devlation I6 $450 an d that the amounts 1etunded follow a normal probability distribution. a. What percont of the refunde aro more th an $3,100? (Round the Intermediate velues to 2 decimal places. Round your answer to 2 decimal places) Percert 0.25 % b. What percent of the refun ds are more th an $3,100 but less th an $3.500? (Round the intermediete values to 2 dec imal places Round your ans wer to 2 decimal places) Peroert c. What percent of the retun ds are more th an $2,250 but less than $3.500? (Round the inter mediate val ues to 2 decimal places Round your answer to 2 decimal places) PeroartIn the final round of a TV game show, contestantshave a chance to increase their current winnings of$1 million to $2 million. If they are wrong, theirprize is decreased to $500,000. A contestant thinkshis guess will be right 50% of the time. Should heplay? What is the lowest probability of a correctguess that would make playing profitable?
- Many decision problems have the following simplestructure. A decision maker has two possible decisions, 1 and 2. If decision 1 is made, a sure cost of c isincurred. If decision 2 is made, there are two possibleoutcomes, with costs c1 and c2 and probabilities p and1 2 p. We assume that c1 , c , c2. The idea is thatdecision 1, the riskless decision, has a moderate cost,whereas decision 2, the risky decision, has a low costc1 or a high cost c2.a. Calculate the expected cost from the riskydecision.b. List as many scenarios as you can think of thathave this structure. (Here’s an example to get youstarted. Think of insurance, where you pay a surepremium to avoid a large possible loss.) For eachof these scenarios, indicate whether you wouldbase your decision on EMV or on expected utility. Ayça and Barış are playing a game and following payoff matrix is for the payoffs of Ayça. Answer the questions according to the following payoff matrix. a) What is the probability that the value of the game is 10?When a pair of dice is tossed, the results may be any whole number from 2 through 12. In the game of craps one can win by tossing either a 7 or an 11 on the first roll. What is the probability of doing this?
- 3. Find the saddle point, if it exists, for the following game. (b) Solve the following game by using the principle of dominance and find the probabilities of strategies for each player and the value of the game. Player B Player A II III IV V 3 4 4 II 2 4 III 4 4 IV 4 4 20 2420 87609. The probability of a woman having a baby boy is 50% and that of having a girl is also 50% What is the probability that a woman who has three children will have three boys? of T. 10. Lebo has 3 blue pens, 2 red pens, 5 black pens and 2 pencils in his pencil case. a. What is the probability that he takes a black pen? b. What is the probability that he takes an item that is not a black pen? 11. One card is drawn from a deck of 52 cards. What is the probability that the card will be a. red or an ace? b. a king of hearts? Samsung Quad Camera Shot with my Galaxy. A2.1sWhen playing roulette at a casino, a gambler is trying to decide whether to bet $10 on the number 30 or to bet $10 that the outcome is any one of the three possibilities 00, 0, or 1. 3 The gambler knows that the expected value of the $10 bet for a single number is - 53¢. For the $10 bet that the outcome is 00, 0, or 1, there is a probability of 38 of making a net profit of $30 and a probability of losing $10. 35 38 a. Find the expected value for the $10 bet that the outcome is 00, 0, or 1. b. Which bet is better: a $10 bet on the number 30 or a $10 bet that the outcome is any one of the numbers 00, 0, or 1? Why? a. The expected value is $. (Round to the nearest cent as needed.) b. Since the expected value of the bet on the number 30 is C than the expected value for the bet that the outcome is 00, 0, or 1, the bet on is better.
- 5.100 Tossing a die. You are tossing a balanced die that has probability 1/6 of coming up 1 on each toss. Tosses are independent. We are interested in how long we must wait to get the first 1. (a) The probability of a 1 on the first toss is 1/6. What is the probability that the first toss is not a 1 and the second toss is a 1? (b) What is the probability that the first two tosses are not 1s and the third toss is a 1? This is the probability that the first 1 occurs on the third toss. 4 (c) Now you see the pattern. What is the probability that the first 1 occurs on the fourth toss? On the fifth toss?1. Consider you toss two dices separately, and you get whatever the number above the dice. You know that the first dice is fair, but there is a 0.30 probability that outcome will be 6, and 0.30 probability that outcome will be 1 in the second dice. Each of the other outcomes has a probability 0.10 for the second dice. Which dice has the higher variance?5. Probability help me uhuhuhuh