ykobe23 Posted January 16, 2012 Report Share Posted January 16, 2012 (edited) Is there an equation to figure out the probability that Ann wins for a given amount of rolls each player gets? for example if you want to know what is the probability that Ann wins if both Ann and Bob roll 4 times. there's got to be a simple equation to figure it out. Otherwise its going to take ALOT of calculating to do. If Ann and bob roll once, the probability is 15/36If Ann rolls twice and Bob rolls once, the probability is 125/216If Ann and Bob each roll twice, the probability is 505/1296So based on that I know that the denominator of the equation is 6^(A) times 6^(B)(A = number of rolls Ann gets, B = number of rolls Bob gets)But I have no Idea how to figure out what the numerator would be.Any Help? yes there is a formula, but it is very complicated. since i did this portfolio, i'm less willing to give out much guidance. my one and only hint: sigma notation.In terms of what variables did you get your formula and a formula for what did you find ? Did you find a formula for the probability for a player to win with n players and n trials or two separate? or something else ? Edited January 16, 2012 by ykobe23 Reply Link to post Share on other sites More sharing options...
IBCONQUERER Posted January 27, 2012 Report Share Posted January 27, 2012 Just to offer abit of a hint for the 2 players rolling twice think of sigma notation and quadratics! Reply Link to post Share on other sites More sharing options...
zakrzi Posted February 22, 2012 Report Share Posted February 22, 2012 Can anyone help me with the last part of portfolio which is a consideration over multiple players? Please, I'm stuck here. Any help would be highly appreciated. Reply Link to post Share on other sites More sharing options...
IB Smacher Glau Posted March 4, 2012 Report Share Posted March 4, 2012 If Ann rolls twic the probability is 125/216 how Reply Link to post Share on other sites More sharing options...
Dinstruction Posted March 13, 2012 Report Share Posted March 13, 2012 I'm about to start this IA, but the problem is that I don't see how I can account for things like errors or limitations because the problem is entirely probability. Also, when "applying the model to other situations," do the suggestions for accounting for extra players or multiple rolls count? 1 Reply Link to post Share on other sites More sharing options...
Lesya Posted March 14, 2012 Report Share Posted March 14, 2012 well, i think multiple player connected with denominator... be hohest, i have a problem with the 3-5... can anyone inspire me and provide a help in these maters? pleeeeeeeeease... Reply Link to post Share on other sites More sharing options...
IBCONQUERER Posted March 14, 2012 Report Share Posted March 14, 2012 Its fairly simple when both roll twice, you should get some pattern use a table for different numbers in each table vary what bob gets on his first roll so basically u shud get 6 tables and from that u can calculate ann's probability of winning in each and every case! then at the end ull get some pattern I'll offer you a hint it has something to do with cubics, I used matrices in my case and then used graphs! My teacher seems to reject the cost/probability hypothesis he says its something to do with expectation, anyone got ny ideas of how I would go about it with expectation? Reply Link to post Share on other sites More sharing options...
IBCONQUERER Posted March 14, 2012 Report Share Posted March 14, 2012 apparently the bank's probability of winning doesnt matter because the bank receives a cost for every game, regardless of whether or not the player is going to win? Reply Link to post Share on other sites More sharing options...
IBCONQUERER Posted March 14, 2012 Report Share Posted March 14, 2012 This is how I've done it, I dont know if its rightif cost > probability of player winning x payout then the game favours the bankif cost < the game favours the playerif its equal its fair!And also r we allowed to choose the probability, dont we have to use the probability that we get from the first bullet point coz theyre both rolling twice! Anyway the casino would never agree to have a game where theyre chances of having to pay the player r more its not profitable for them! Reply Link to post Share on other sites More sharing options...
Dinstruction Posted March 15, 2012 Report Share Posted March 15, 2012 My teacher recommended creating a simulation using Java (which I'm capable of) and running it multiple times, analyzing the results. I hope this is adequate usage of technology. Reply Link to post Share on other sites More sharing options...
IB Smacher Glau Posted March 15, 2012 Report Share Posted March 15, 2012 My teacher recommended creating a simulation using Java (which I'm capable of) and running it multiple times, analyzing the results. I hope this is adequate usage of technology.I Take CS .. we use Blue J .. how are you going to do this using Java ?? Reply Link to post Share on other sites More sharing options...
IBCONQUERER Posted March 15, 2012 Report Share Posted March 15, 2012 My teacher recommended creating a simulation using Java (which I'm capable of) and running it multiple times, analyzing the results. I hope this is adequate usage of technology.My teacher recommended creating a simulation using Java (which I'm capable of) and running it multiple times, analyzing the results. I hope this is adequate usage of technology.wow, i dont even understand what that means at all!! Reply Link to post Share on other sites More sharing options...
Dinstruction Posted March 15, 2012 Report Share Posted March 15, 2012 My teacher recommended creating a simulation using Java (which I'm capable of) and running it multiple times, analyzing the results. I hope this is adequate usage of technology.I Take CS .. we use Blue J .. how are you going to do this using Java ??I use JCreator. I'm not familiar with Blue J, so I don't know why you would see that as unfeasable. Reply Link to post Share on other sites More sharing options...
IBCONQUERER Posted March 17, 2012 Report Share Posted March 17, 2012 if u look at criterion D it says interpret your model, in this case I'm not sure how you do it?? Because all you have calculated is for 3 cases, and when you do get the general formula for any case..you'll have a very limited amount of data to test the fit of the model??Oh and does using tables obviously this task I used an innumerable amount of them, contribute to marks in technology criteria? Coz its obvious without tables it would be pretty difficult to do the first 3 bullets! Reply Link to post Share on other sites More sharing options...
t1nspire Posted March 17, 2012 Report Share Posted March 17, 2012 how did you guys get 125/216 probability when ann rolls twice and bob rolls once Reply Link to post Share on other sites More sharing options...
IBCONQUERER Posted March 17, 2012 Report Share Posted March 17, 2012 calculate Bob's probability of winning when he rolls a 1 2 3 4 5 or 6 by figuring how many combinations ann can roll for bob to win in each case you'll see some pattern and then ann's probability is just 1 - bob's probability! Reply Link to post Share on other sites More sharing options...
IB Smacher Glau Posted March 19, 2012 Report Share Posted March 19, 2012 IMPORTANTdid anyone draw two tree diagram?? one for both playing once , while other for one playing twice while other onceand then a large table when player both play twice 1 Reply Link to post Share on other sites More sharing options...
arra Posted March 21, 2012 Report Share Posted March 21, 2012 I sat for a while and actually managed to get a general formula that I know is right for the first four values (11 21 12 22) because I had already calculated them but it's quite complicated and I'm not even sure it's correct beyond that. Teacher is rest but probability is not her thing so not particularly sure how to check it, I mean I know that my logic is right just the formula does nottt look too pretty. Reply Link to post Share on other sites More sharing options...
Dinstruction Posted March 23, 2012 Report Share Posted March 23, 2012 (edited) I figured out the formula for the general case where Ann rolls x times and Bob rolls y times. Here's some help:First, let's consider Bob's score.There are six possible cases for Ann's number, 1 to 6. Say her score is k. What is the probability that Ann's score is equal to k (let's just call it P(A=k) for now) AND that all of Bob's rolls are less than k? This tells us the probability that Ann will win given her score is k. Your final answer is the sum from k = 1 to 6.To actually find P(A=k), consider the case when k=1. There's only one possibility that all of her rolls are equal to one.Now find P(A=2). This means that we find that all of her rolls have the outcome P(1 or 2) (and we do this x times). However, we need to ensure that at least one of her rolls is equal to 2. So we need to subtract the case when all of her rolls are equal to 1.And we repeat this process until P(A=6). You should probably see the telescoping series. The formula isn't that bad, but it takes a little bit of thinking. Edited March 23, 2012 by Dinstruction 3 Reply Link to post Share on other sites More sharing options...
IB Smacher Glau Posted March 24, 2012 Report Share Posted March 24, 2012 I just creating other model, other than the formula you will get credit ! ( it's mentioned on the criteria ) .. for example creating a module in the Casino case. Reply Link to post Share on other sites More sharing options...
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