A decision maker usually has a choice among several possible alternative acts. For each alternative act, there are many possible results called states of occurrence. True or False True False es

In a game, two coins are tossed. If either of the coins comes up heads, you have won a prize. To claim the prize, you must point to one of your coins that is a head and say 'look, that coin's a head, I've won'. You watch Fred play the game. He tosses the two coins, and he points to a coin and says 'look, that coin's a head, I've won'. What is the probability that the other coin is a head?

Suppose that A E Mmxn(R) is a matrix of user ratings of various movies (on a scale of 1 to 5). Suppose we have computed the SVD of А, and decided to keep the 10 largest singular values as the most important determining factors for a user's choice of movie. Suppose also that a new user has joined the movie subscription service, and has rated some, but not all, of the movies. To predict how this new user will rate other movies (and thus, to determine which ones to recommend), all movies the user has not watched are assigned the average rating for that movie given by all users to form a new matrix A' E M(m+1)xn(R), and the rank-10 approximation of A' is computed from its SVD. The values in the approximation to A' are taken as the predicted ratings for the new user. Given this procedure, which of the following conclusions is most correct?

Overbooking is the practice of selling more items than are currently available. Overbooking is common in the travel industry; it allows a vehicle (airline, train, bus, cruise ship, hotel, and so forth) to operate at or near capacity, despite cancellations, no-shows, or late arrivals. Overselling is when more confirmed customers show up to use the vehicle than there is space available. When this happens, at least one customer will be denied the service that they paid for, either voluntarily (sometimes with an incentive provided by the supplier) or involuntarily. This is called getting "bumped." Suppose that for a particular flight, an airline believes that 2% of ticket holders do not make the flight. The jet making the trip holds 189 passengers. If the airline sells 192 tickets, what is the probability that the flight will be oversold and they will have to bump a passenger? Assume that cancellations are independent. Calculate the probabilities that one, two, and three people will be…

A favorite casino game of dice “craps” is played in the following manner: A player starts by rolling a pair of balanced dice. If the roll (the sum of two numbers showing on the dice) results in a 7 or 11, the player wins. If the roll results in a 2 or 3 (called “craps”) the player loses. For any other roll outcome, the player continues to throw the dice until the original roll outcome recurs (in which case the player wins) or until a 7 occurs (in which case the player loses). When answering the following questions, you can use this outcome chart for the roll of two dice: Provide the probability answers in fraction and in decimal forms rounded to 4 digits.     A. List the possible outcomes (sample space) for winning on the first roll of the dice.   B. What is the probability that a player wins the game on the first roll of the dice?   C. List the possible outcomes (sample space) for losing on the first roll of the dice.   D. What is the probability that a player loses the game on the…

The events driving a sedan and driving in an attentive style are approximately independent because P(attentive | sedan) ≈ P(attentive).  The events driving a sedan and driving in an attentive style are not independent because P(sedan | attentive) ≈ P(sedan).  The events driving a sedan and driving in an attentive style are approximately independent because P(sedan | attentive) ≈ P(sedan).  The events driving a sedan and driving in an attentive style are not independent because P(attentive | sedan) ≈ P(attentive).