AI: Two events, A and B, are mutually exclusive and each has a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is _____. a. 1 b. 0 c. any value between 0 and 1 d. any positive value
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Two events, A and B, are mutually exclusive and each has a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is _____.
a. 1b. 0c. any value between 0 and 1d. any positive value
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- In this version of dice blackjack, you toss a single die repeatedly and add up the sum of your dice tosses. Your goal is to come as close as possible to a total of 7 without going over. You may stop at any time. If your total is 8 or more, you lose. If your total is 7 or less, the house then tosses the die repeatedly. The house stops as soon as its total is 4 or more. If the house totals 8 or more, you win. Otherwise, the higher total wins. If there is a tie, the house wins. Consider the following strategies: Keep tossing until your total is 3 or more. Keep tossing until your total is 4 or more. Keep tossing until your total is 5 or more. Keep tossing until your total is 6 or more. Keep tossing until your total is 7 or more. For example, suppose you keep tossing until your total is 4 or more. Here are some examples of how the game might go: You toss a 2 and then a 3 and stop for total of 5. The house tosses a 3 and then a 2. You lose because a tie goes to the house. You toss a 3 and then a 6. You lose. You toss a 6 and stop. The house tosses a 3 and then a 2. You win. You toss a 3 and then a 4 for total of 7. The house tosses a 3 and then a 5. You win. Note that only 4 tosses need to be generated for the house, but more tosses might need to be generated for you, depending on your strategy. Develop a simulation and run it for at least 1000 iterations for each of the strategies listed previously. For each strategy, what are the two values so that you are 95% sure that your probability of winning is between these two values? Which of the five strategies appears to be best?If events X and Y are mutually exclusive then A- P(X)P(Y) = 0 B- they are independent events C- their joint probability is zero D- P(X)P(Y) = P(X | Y)Suppose that you have two four-sided dice that are each equally weighted (i.e. equal chance of any of the four sides landing face up). One of them has values [12.5968, 2, -2 and -12.5968] , the other [12.5968, 4, -2 and -12.5968] . Which of them has a µ of zero using the probability model approach. 1. [12.5968, 4, -2 and -12.5968] 2. [12.5968, 2, -2 and -12.5968]
- A hospital has three independent fire alarm systems, with reliabilities of .95, .97, and .99. In the event of a fire, what is the probability that a warning would be given?Habard’s, a chain of hardware stores, sells a variety of tools and home repair items.One of their best wrenches sells for $5.50. Habard’s will include a three-year freereplacement warranty for an additional $1.50. The wrench is expected to be subject to heavy use and, based on past experience, will fail randomly at a rate of oneevery eight years. Is it worth purchasing the warranty?A car repair can be performed either on time or late, and either satisfactoryily or unsatisfactorily. The probability of a repair being on time and satisfactory is 0.26. The probability of a repair being on time is 0.74. The probability of a repair being satisfactory is 0.41. What is the probabilityof a repair being late and unsatisfactory?
- |At the Pleasant Haven Hotel there are 36 rooms. The profit earned when a room is sold for a night is $53. If Pleasant Haven overbooks, by selling more reservaitions than they have rooms and they end up having a customer whose reservation cannot be fulfilled, the loss to Pleasant Haven is $30 for that customer. Regardless of the number of rooms booked, the probability of one no show is 60% and the probability of 2 no shows is 20%. There is zero probability of more than 2 no shows. For a night when requests are exceeding the 36 rooms, what is the optimal number of reservations to accept? Assume there is no penalty for a customer who does not show up, i.e., Pleasant Haven does not make $53 on a customer that is a no show. What is the expected net for booking each of the following: (Net means profit minus any overbooking loss.) 36 customers 37 customers 38 customers What is the best number of book?Non-inventory goods were purchased and delivered on June 15, 2010. Several security interests exist in these goods. Which of the following security interests has priority over the others? Group of answer choices purchase money security interest perfected June 24, 2010 Security interest perfected June 20, 2010 Security interest attached June 15, 2010 Security interest in future goods attached on June 10, 2010A swim club is designing a new pool to replace its old pool. The new pool would need to last for 10 years since the club is planning on relocating after 10 years. A concrete shell would cost $85,000 and last for all 10 years. Another option is to install a vinyl liner that would cost only $70,000 to install. However, the vinyl is not guaranteed to last for all 10 years, and it has a 40% chance of breaking down. Repair of the vinyl would cost $40,000 and would extend the life of the vinyl liner to the 10-year mark. If both options are acceptable to the swim club, which one minimizes cost? Support your answer with drawing a decision tree and provide your calculation.
- 4. From past experience, Anna knows that the probability that her friend will take her to dinner in Orro Resto id 0.7, the probability that they will watch movies is 0.5, and the probability that he will take her to dinner or they will watch movies is 0.9. What is the probability that they will do both? they will do neither? 5. Eight persons enter a supermarket. From the past experience, it is known that 25% of the people entering the supermarket make a purchase. What is the possible values of the random variable X? Construct the probability distribution of X. X P(X=x) What is the probability that 1) at least four persons will make a purchase? 2) two or three persons will make a purchase? 3) a most two persons will make a purchase?true or false 7. The expected utility implies that the decision maker regards this option as being equivalent to a lottery offering a same chance of the best/best outcome (and a complementary probability of the worst/worst outcome)What is false about service level and stock out? Service level and stock out risk are probabilities of mutually exclusive events Service level is the probability of attending the demand and stock out risk it the probability of not attending the demand Service level and stock out risk are inversely related Service level and stock our risk are directly related