My Math Forum Game theory question with 4 variables

 November 1st, 2010, 06:35 AM #1 Newbie   Joined: Nov 2010 Posts: 6 Thanks: 0 Game theory question with 4 variables Variable 1 = 58% probability for positive result Variable 2 = 52% probability for positive result Variable 3 = 53% probability for positive result Variable 4 = 51% probability for positive result You can only have positive ore negative result. These 4 variables is needed to calculate the outcome of the final result. If 2 variables = negative result, and 2 variables = positive result. The outcome will be the same as the beginning result ( feks. If the beginning result is 100 the outcome will be 100) If 1 variables = negative result and 3 variables = positive result. The outcome will be positive ( feks. If the beginning result is 100 the outcome will be above 100). If 3 varibales = negative result and 1 variables = positive result. The outcome will be negative ( feks. If the beginning result is 100 the outcome will be below 100) And so on. What is the probability in percentage to hit = 100, abowe 100 and below 100 ? Thanks alot for any answer
 November 1st, 2010, 09:31 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Game theory question with 4 variables There are 16 possibilities in total: 5 that cause an increase, 5 that cause a decrease, and 6 that cause it to stay the same. With numbers this small, I tend to think you should just calculate them directly.
 November 2nd, 2010, 06:43 AM #3 Newbie   Joined: Nov 2010 Posts: 6 Thanks: 0 Re: Game theory question with 4 variables Thanks for the reply. How did you calculate the answer ?
November 2nd, 2010, 10:32 AM   #4
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Re: Game theory question with 4 variables

Quote:
 Originally Posted by solq4 Thanks for the reply. How did you calculate the answer ?
${4\choose2}=\frac{4!}{2!2!}$ ways of getting a tie, then equal numbers for the others. Alternately, 1 way to have everything go to one side and 4 ways to get all but one; that's 5 for positive and 5 for negative, leaving 6 for ties.

Or you could do both calculations and breathe a sign of relief knowing that "math works".

 November 7th, 2010, 07:56 AM #5 Newbie   Joined: Nov 2010 Posts: 6 Thanks: 0 Re: Game theory question with 4 variables Thanks . How do you do it for excact percentages for getting the results ?
 November 7th, 2010, 09:48 AM #6 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Game theory question with 4 variables For any individual combination, multiply the probabilities for each element, using p if it occurs and 1-p otherwise.

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