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- A bag contains 5 red balls and 3 white balls. If 3 balls are drawn with replacement from the bag, what are the probabilities that. a. 2 balls will be red? b. a least 2 balls will be red?Suppose that Trendy Inc. products a style of a seasonal business suit, Sit-T-Slicker, which has a cost of $500 per unit. The demand during the season for Sit-T-Slicker is generally unknown and could be either: 200, 500, 800, 1100, and 1500 units with equal probabilities. Trendy sells the Sit-T-Slicker suit for $900 per unit during its three-month season, and for $300 per unit when sold after that time. Given the above data, what is the optimal order quantity for the Sit-T-Slicker? What is expected profit? Suppose the probabilities in part a change to 0.05, 0.25, 0.40, 0.25, 0.05 for demand levels 200, 500, 800, 1100, 1500, respectively. What is the optimal order quantity and expected profit in this case? How would better information regarding the demand for the Sit-T-Slicker suit change the data provided in this problem? How would this information affect the answers to part a? Explain.(QUEEN'S SECRET AND GENIES) In old days, there was a queen and she had a secret problem to solve. To get an answer to her secret problem, the queen bought one female and one male genie lamps. The probabilities that her secret problem can be solved by the male and female genies are 0.3 and 0.4 respectively. A Queen looking for divine help. Assume the queen keeps the genies independently away from each other with a fear that both could not harm her, what is the probability that the queen's secret problem is solved by at least one of the genies? Note: Please keep accuracy upto two decimal places.
- A system has six components connected as shown in the following diagram: A Assume A, B, C, D, E, and F function independently. If the probabilities that A, B, C, D, E, and F fail are 0.01, 0.05, 0.02, 0.08, 0.10, and 0.05 respectively, what is the probability that the system fails?104. Two sets of candidates are competing for the positions on the Board of Directors of a company. The probabilities that the first and the second sets will win are O-6 and 0-4 respectively. If the first set wins, the probability of introducing a new product is 0-8 and corresponding probability if the second set wins is 0-3. What is the probability that the product will be introduced ?A system has five components connected as shown in the diagram. Assume A, B, C, D, and E function independently. If the probabilities that A, B, C, D, and E function 0.50, 0.65, 0.75, 0.95, and 0.80 respectively, what is the probability that the system fails? 50 .65 A B 1.75 с 95 D E
- From a large survey of customers using a chain of coffee shops, 60% of the customers are male, 50% purchase food, 15% are both Male and purchase food. What are the probabilities that: A customer is both female and purchases food? A female customer purchases food? A customer purchasing food is female?On Mr. Casper's debate team at Thunderbird High School, 20% of the members are Sophomores, 35% are Juniors and 45% are Seniors. A team member is selected randomly to give the closing argument for the team. If a sophomore gives the closing argument, the team has a probability of 0.25 of winning the debate. If a junior gives the closing argument, the probability of winning is 0.6. If a senior closes, the probability of winning is 0.85. (a) Find the probability that the team wins the debate. b sketch a tree diagram to model this process2b) Find zo for the following probabilities: i) P(Z > Zo) - 0.25 O-0.67 O o 0.67 O 0.5 Jimmy and Rosalynn Carter celebrate 76 years of marm to
