Three cards are drawn with replacement from a standard deck. What is the probability that the first card will be a club, the second card will be a red card, and the third card will be the six of hearts? Express your answer as a fraction or a decimal number rounded to four decimal places.
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- Two cards are drawn from a standard deck without replacement. What is the probability that the first card is a diamond and the second card is red? (Round your answer to three decimal places.)the video link is: https://www.youtube.com/watch?v=aqEz6kvXhc8please give me detailed solutions and calculations, thank you!A wheel of fortune in a gambling casino has 54 different slots in which the wheel pointer can stop. Four of the 54 slots contain the number 9. For $3 bet on hitting a 9, if he or she succeeds, the gambler wins $16 plus return of the $3 bet. What is the expected value of this gambling game? (Present your answer in dollars with 2 decimal places but without $ sign)
- Carl is an insurance representative who attempts to sell home insurance to 140 customers per year. If he expects 65.1% of these sales to be successful, how many sales will be successful? Provide your answer to two decimal places.Question 5 You negotiate with a retailer over a contract according to which the retailer would buy a large fraction of your current production for next year. The retailer is perfectly informed about consumer demand, but you do not know whether demand is high or low. You only know that the probability for high demand is 80%. If demand is high, the retailer's profit is £5 million minus what he pays to you according to your contract. If demand is low, the retailer's profit is £3 million minus what he pays to you. Your costs of producing the output specified in the contract are £1 million. You can make sequential offers for the retailer's total payment for you to deliver a fixed quantity of your production. As you know that your competitor is also seeking a similar contract with this retailer, and the retailer can only supply one firm due to limited shelf space, you know that you can only make at most two offers. If your first offer is rejected, the retailer will strike the deal with your…In the final round of a TV game show, contestants have a chance to increase their current winnings of$1 million to $2 million. If they are wrong, their prize is decreased to $500,000. A contestant thinks his guess will be right 50% of the time. Should he play? What is the lowest probability of a correct guess that would make playing profitable?
- A new product is built and ready to launch. If successful, it will lead to a profit of $50,000. If it is unsuccessful, it will lead to a loss of $30,000. What probability of success would make the company indifferent about launching the product? Enter as a decimal (not a percentage).A 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 the final round of a TV game show, contestants have a chance to increase their current winnings of $1 million dollars to $2 million dollars. If they are wrong, their prize is decreased to $500,000. The contestant thinks his guess will be right 50% of the time. Should he play? What is the lowest probability of a correct guess that would make playing profitable?
- You are considering a $500,000 investment in the fast-food industry and have narrowed your choice to either a McDonald's or a Penn Station East Coast Subs franchise. McDonald's indicates that, based on the location where you are proposing to open a new restaurant, there is a 25 percent probability that aggregate 10-year profits (net of the initial investment) will be $16 million, a 50 percent probability that profits will be $8 million, and a 25 percent probability that profits will be -$1.6 million. The aggregate 10-year profit projections (net of the initial investment) for a Penn Station East Coast Subs franchise is $48 million with a 2.5 percent probability, $8 million with a 95 percent probability, and -$48 million with a 2.5 percent probability. Considering both the risk and expected profitability of these two investment opportunities, which is the better investment? Explain carefully.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 16/52If you choose two people at random, what is the probability that both have the same blood type?
