A poker hand (5 cards) is drawn from an ordinary deck of 52 cards. Find the probability of each event, showing your reasoning carefully. a. The first four cards are aces. b. Any four cards are the four aces.
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A poker hand (5 cards) is drawn from an ordinary deck of 52 cards. Find the probability of each event, showing your reasoning carefully.
a. The first four cards are aces.
b. Any four cards are the four aces.
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- Decisions Involving Uncertainty - End of Chapter Problem You're a project manager overseeing five teams that are developing a new app. Each team must complete their work by July 1 in order to release the app by the end of the year. Based on your work managing the project, you know that each team has about a 75% chance of meeting the deadline. a. The probability that your firm will complete the project by the end of the year is b. Suppose that before you calculate the probability of completing the project, you walk into a weekly status meeting with the CEO. When she asks you for your "gut feeling" about the probability of finishing the project by the end of the year, you respond with an answer that exhibits the anchoring bias. Your response will likely be, "About 70%." "About 90%." "About 25%."QUESTION 26 A deck of 52 playing cards consists of 4 suites: clubs, spades, hearts, and diamonds. Each suite consists of 13 cards. Draw one from a deck of cards. Let A=a card "2" is drawn, B=a "diamond" card is drawn. Which is the value of P(A and B), i.e., {probability that the card drawn is "diamond" and "2"} ? 1/52 4/52 13/52 16/52The 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? Pass uny Patriots D Pass .4, .6 D Run .9,.1 .8,.2 .5,.5 Pass Run Opponent D Pass D Run .06, .94 .32, .68 .8,.2 .5,.5
- For the following questions consider this setting. The deciding shot in a soccer game comes down to a penalty shot. If the goal-keeper jumps in one corner and the striker shots the ball in the other, then it is a goal. If the goalie jumps left and the striker shoots left, then it is a goal with probability 1/3. If the goalie jumps right and the striker shots right, it is goal with probability 2/3. QUESTION Say the goalie's strategy is to jump left with probability 1 and the striker shoots left with probability 0.5, then the probability of a goal is (round to two digits) QUESTION If the striker shoots in either corner with probability 0.5 and the goalie likewise shoots in either corner with probability 0.5, then the probability of a goal is (round to 2 digits)1. A dealer decides to sell a rare book by means of an English auction with a reservation price of 54. There are two bidders. The dealer believes that there are only three possible values, 90, 54, and 45, that each bidder’s willingness to pay might take. Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities for each of the two bidders are independent of the other’s valuation. Assuming that the two bidders bid rationally and do not collude, the dealer’s expected revenue is approximately ______. 2. A seller knows that there are two bidders for the object he is selling. He believes that with probability 1/2, one has a buyer value of 5 and the other has a buyer value of 10 and with probability 1/2, one has a buyer value of 8 and the other has a buyer value of 15. He knows that bidders will want to buy the object so long as they can get it for their buyer value or less. He sells it in an English auction with a reserve price which he must…. 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?
- 2. Calculate the probabilities that a. the battery life is between 7.5 and 8 hours; and b. the battery life is less than 8 hours. Are these two probabilities different? Explain why or why not. 3. Suppose that you randomly picked 100 iPhones and calculated the average battery life for these phones. Provide your best guess of the value of the average.QUESTION 24 A deck of 52 playing cards consists of 4 suites: clubs, spades, hearts, and diamonds. Each suite consists of 13 cards. Draw one from a deck of cards. Let A=a card "2" is drawn, B=a "diamond" card is drawn. Which is the value of P(A|B), i.e., {probability that the card drawn is "2" given that we have known it is "diamond"} ? 1/52 1/4 1/13 16/52A lottery has a grand prize of $1,000,000, 2 runner-up prizes of $100,000 each, 6 third-place prizes of $10,000 each, and 19 consolation prizes of $1,000 each. If a 4 million tickets are sold for $1 each, and the probability of any ticket winning is the same as that of any other winning, find the expected return on a $1 ticket. (Round your answer to 2 decimal places.
- In a final round of a MegaMillion TV show, a contestant has won $1 millionand has a chance of doubling the reward. If he loses his winnings drop to$500,000. The contestant thinks his chances of winning are 50%. Should heplay? What is the lowest probability of a correct guess that will make his betprofitable? Show workYou work at a mechanic shop. 40% of cars that come in have a flat tire. If there are 50 cars in the shop, what is the probability that more than 30 have a flat tire? Round to three decimal points.In 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?