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Data Generator
Generate data sets with continuous, categorical, grouped and correlated data. Great for creating data sets for examples and for quality assurance testing. Data sets are created in standard .CSV format so they can be opened in most statistical programs such as SAS, SPSS, WINKS and into spreadsheet programs such as Microsoft Excel. Order now.
Monty Hall Problem
in Probability
These tutorials briefly explain the use and interpretation of standard statistical analysis techniques using popular data analysis software including SAS Statistics software, SPSS, WINKS Statistics analysis software and Microsoft Excel (data analysis tool).
Choose Door Number 1, 2, or 3
The 3-Door Probability Puzzle (Monty Hall Paradox)
The 3-Door Puzzle (also called the Monty Hall Paradox) is a probability puzzle that got its name from a popular television game show Let's Make a Deal with host Monty Hall.
Description of problem
Suppose there are three doors. Behind one door is a great prize, a new automobile. Behind the other two doors is a not-so-good prize, a giant pickle. You get to select one door. The game host will then open another door to show you that there is a pickle behind that door. Now you have to choose to keep the door you originally selected, or switch to the other unopened door. From a probability basis, does it make a difference if you keep the original door or switch?
The problem received much publicity when the question to stay or switch was posed to the well-known (Guinness Book of World Records highest IQ) Marilyn vos Savant in her “Ask Marilyn” column in the September 9, 1990 issue of Parade Magazine.
Common sense indicates that you have an equal chance of the big prize being behind either of the two remaining doors, so there is a 50-50 chance, and from a probability standpoint, it makes no difference if you stay or switch.
However, vos Savant claimed that the best strategy was to switch. This set off a series of letters from a number of mathematicians challenging the claim.Solution
Assuming the car is randomly placed behind one of the three doors, the solution to the controversy can be answered in either of two ways.Answer 1 – Use a computer program -- Experiment to see if either way makes a difference. Use the WINKS SDA program (Analyze, Demonstration and Simulations) to run a simulations of 100, 1000 or more games -- select to either switch or stay the same, and see how they compare.
Answer 2—Use probability calculations: Create a sample space of outcomes – these are the only possible outcomes. This assumes that you choose a door at random.
You switch – you lose
You stay – you win
Case 2 – You choose X and Car is behind door Y – Host must open Door Z
You switch – you win
You stay – you lose
Case 3 – You choose X and car is behind door Z – Host opens door Y
You switch – you win
You stay – You lose
Since the sample space has 3 outcomes, each outcome occurs with a 1/3 probability. Note that in 2 outcomes you win and in one you lose. Thus, the best strategy is to switch, which yields a probability of 2/3 rather than to stay (1/3)
For more information...
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