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September 27th, 2012, 12:46 AM  #1 
Newbie Joined: Sep 2012 Posts: 3 Thanks: 0  Need help to find minimal cost to complete a task
There is a task that it is either success or failure with fixed probability. We need to pay more in order to get better success rate. If there are sufficient resources, we could make sure it can be success. Success rate (P)  Cost (C) Code: 20%  $10 40%  $20 60%  $40 80%  $80 100%  $160 Code: 1st trial: $80, failure 2nd trial: $20, failure 3rd trial: $$80, success We would like to find the most costeffective solution (minimum cost) in general. Say, "Given $100, we have 90% confident to complete the task". Is it able to do some calculation for that by providing success rate and cost? Thank you for help. 
September 27th, 2012, 01:44 AM  #2 
Senior Member Joined: Aug 2012 Posts: 229 Thanks: 3  Re: Need help to find minimal cost to complete a task
Hey summoner. What kind of conditions do you need? You need to specify conditions like for example what the probability needs to be (and for how many trials). Once you do this, you have a function for the Cost given the number of trials and the possibilities and then you want to consider how to make sure that you get a minimum probability for so many successes. In general you can have many different kinds of probabilities for each trial: for example you can assign the first with one probability, the second with another and so on. For general probabilities you can use what is called a Probability Generating Function to get the PDF of the number of successes of arbitrary success and failure rates. 
September 27th, 2012, 02:36 AM  #3 
Newbie Joined: Sep 2012 Posts: 3 Thanks: 0  Re: Need help to find minimal cost to complete a task
Thanks for your reply. The number trial is unlimited and we need to find the best solution with minimum cost. Say assuming we have 100 task, I want a cheap solution with 80% confidence to succeed. I will check Probabilitygenerating function that you have suggested. Thanks. 
November 6th, 2012, 05:08 PM  #4 
Newbie Joined: Sep 2012 Posts: 3 Thanks: 0  Re: Need help to find minimal cost to complete a task
I would like to simplify the case by restricting the choice that a user can only choose either 1 scheme to take the task. Say for example, we can now choose the following 2 scheme. User can do a trial with same scheme until they get success Success rate (P)  Cost (C) Code: 2%  $1 20%  $10 For example, Code: 1st trial: 20% success by paying $10, failure 2nd trial: 20% success by paying $10, failure 3rd trial: 20% success by paying $10, success Cost = 3*10 = $30 Code: 1st trial: 2% success by paying $1, failure 2nd trial: 2% success by paying $1, failure 3rd trial: 2% success by paying $1, failure 4th trial: 2% success by paying $1, failure ... 20th trial: 2% success by paying $1, success Cost = 20*1 = $20 It is supposed to be related to geometric series for getting 80% success in n trials. Code: Percent(S) = p + (1p)*p + (1p)^2*p + ... Cost = C * S 

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