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July 12th, 2017, 07:17 AM  #1 
Newbie Joined: Jul 2017 From: Istanbul Posts: 5 Thanks: 0  Binary Probability Formula
Hi I don't good at math so I need a formula. For example there are 4 cells ABCD and their probabilities %40%60%45%55. I want to calculate which binary is the best, AB or CD?

July 12th, 2017, 04:22 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,835 Thanks: 733 
Your description is is very unclear. is"" supposed to be a minus sign or a connector? The % add up to 200  this doesn't make sense.

July 12th, 2017, 06:54 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond 
That depends on what assumptions one makes about the data. If the percentages are the chances that, say, four different shooters  each shooting at their own target  are successful, then the pair (C, D) is (possibly) the 'best binary' as 0.45 * 0.55 = 0.2475, whereas 0.40 * 0.60 = 0.24. Whether or not that's a correct interpretation I'll leave to the OP to decide. 
July 14th, 2017, 04:52 AM  #4 
Newbie Joined: Jul 2017 From: Istanbul Posts: 5 Thanks: 0 
They are separate A B C D and %40 %60 %45 %55 and yes I don't care other datas percentages are the chances. So if we change the question A B C D E F... %40 %60 %45 %55 %62 %43... what we need to do is multiply these percentages? If we compare them A B C and D E F 0.40*0.60*0.45 vs 0.55*0.62*0.43 ?

July 14th, 2017, 01:15 PM  #5  
Global Moderator Joined: May 2007 Posts: 6,835 Thanks: 733  Quote:
When you say A B C do you mean independent variables and all are 1? You need to clarify your question!  
July 14th, 2017, 03:55 PM  #6 
Newbie Joined: Jul 2017 From: Istanbul Posts: 5 Thanks: 0 
I got it. For example we have 10 old pistol and each of them has a stuck problem they can't always get fired. Let's say we know their fire chances like first one has %85 other one %92 chance.... Think simple I don't want details other datas, it can be possible to calculate that we took 10 pistol 5 to 5 and shoot to bottles. Which team will win?
Last edited by Karma; July 14th, 2017 at 03:57 PM. 
July 15th, 2017, 01:58 PM  #7 
Global Moderator Joined: May 2007 Posts: 6,835 Thanks: 733 
You can the probabilities using the binomial distribution to get the probability for each pistol that it will be successful for n out of 5, where n ranges from 0 to 5. prob (n hits out of 5) = $\displaystyle \binom{5}{n}p^n(1p)^{5n}$ p is the probability that a pistol fires. You can do the calculation for each pistol and compare. 
July 16th, 2017, 07:44 AM  #8 
Newbie Joined: Jul 2017 From: Istanbul Posts: 5 Thanks: 0 
Alright I'll change the question. For example I have one dice, one coin and 4 different balls(one of them blue). I throw them at the same time and want to Blue ball, tails, and number 5. Their probabilities 1/4 1/2 1/6 right? What is the total probability?

July 16th, 2017, 08:41 AM  #9 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 552 
$\dfrac{1}{4} * \dfrac{1}{2} * \dfrac{1}{6} = \dfrac{1}{48} \approx 2.1\%.$ The logic is that there are 4 different possible results with the respect to the ball, 2 different possible results with the respect to the coin, and 6 different possible results with the respect to the die, or 48 equally likely possibilities in all. So any one possibility has a probability of 1/48. The formula to remember is: $\text {A and B are independent events} \iff P(A\ and\ B) = P(A) * P(B).$ Last edited by JeffM1; July 16th, 2017 at 08:46 AM. 
July 17th, 2017, 01:28 PM  #10 
Newbie Joined: Jul 2017 From: Istanbul Posts: 5 Thanks: 0 
Thanks


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