Reference no: EM131754388
(The Monty Hall problem)
Suppose there are three doors, labeled A, B, and C. A new car is behind one of the three doors, but you don't know which. You select one of the doors, say, door A. The host then opens one of doors B or C, as follows: If the car is behind B, then they open C; if the car is behind C, then they open B; if the car is behind A, then they open either B or C with probability 1/2 each. (In any case, the door opened by the host will not have the car behind it.) The host then gives you the option of either sticking with your original door choice (i.e., A), or switching to the remaining unopened door (i.e., whichever of B or C the host did not open). You then win (i.e., get to keep the car) if and only if the car is behind your final door selection. (Source: Parade Magazine, "Ask Marilyn" column, September 9, 1990.) Suppose for definiteness that the host opens door B.
(a) If you stick with your original choice (i.e., door A), conditional on the host having opened door B, then what is your probability of winning? (Hint: First condition on the true location of the car. Then use Theorem 1.5.2.)
(b) If you switch to the remaining door (i.e., door C), conditional on the host having opened door B, then what is your probability of winning?
(c) Do you find the result of parts (a) and (b) surprising? How could you design a physical experiment to verify the result?
(d) Suppose we change the rules so that, if you originally chose A and the car was indeed behind A, then the host always opens door B. How would the answers to parts (a) and (b) change in this case?
(e) Suppose we change the rules so that, if you originally chose A, then the host always opens door B no matter where the car is. We then condition on the fact that door B happened not to have a car behind it. How would the answers to parts (a) and (b) change in this case?
|
What challenges or obstacles does the firm encounter
: What challenges or obstacles does the firm encounter in using Application Portfolio Management? Your paper must follow APA style guidelines, as appropriate.
|
|
The game of craps
: The game of craps is played by rolling two fair, six-sided dice. On the first roll, if the sum of the two numbers showing equals 2, 3, or 12
|
|
Determine the distribution of customers
: On average last year a local leisure centre had 230 customers per day, standard deviation 27, and the distribution of customers was found to be Normal.
|
|
Discuss leadership in problem-oriented policing
: As a police officer, describe how important it is to support community problem-solving and broken windows policing by applying problem-solving techniques.
|
|
The monty hall problem
: Suppose there are three doors, labeled A, B, and C. A new car is behind one of the three doors, but you don't know which. You select one of the doors
|
|
Number of support systems to carry on business operations
: Company strategies can’t be implemented or executed well without a number of support systems to carry on business operations
|
|
Compute the unit product cost for one gamelan
: Compute the unit product cost for one gamelan, Assume that the company uses variable costing. Compute the unit product cost for one gamelan
|
|
An approach for balancing the issues of individual rights
: Determine a philosophy and approach for balancing the use of reward and punishment in criminal justice.
|
|
Analyze a method for consolidating core network services
: Explain the key considerations behind establishing trust relationships between the two domains. Analyze a method for consolidating Core Network services.
|