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How to find Probability of three Systems

  • #1
  • First Post: Jul 6, 2015 12:02am Jul 6, 2015 12:02am
Hi looking for a mathematical help here.

If there are 3 independent systems A, B & C. Each has wining rate of 60% & loosing rate of 40%.
Now I find following conditions. But for the rest need help.

Probability of loosing 3 systems all together = A ∩ B ∩ C = 29%
Probability of wining 3 systems all together = A ∩ B ∩ C = 5%

There is another way I saw on net is , probability of loosing 3 systems = 0.4*0.4*0.4 = 0.064
Probability of winning 3 systems = 0.6*0.6*0.6= 0.216

Which one is correct?

Probability of winning of 2 systems all together & losing 1 system = ??
Probability of losing of 2 systems all together & winning 1 system = ??

Thank you
Please share the formula also.
Discussion is an exchange of knowledge;argument is an exchange of ignorance
  • #2
  • Jul 8, 2015 1:04pm Jul 8, 2015 1:04pm
Hi PipPirates.

Your assumption that the 3 systems are independent is important for this math to work out. This implies that the 3 systems have zero correlation to each other. Let's just work out all the 3 system possibilities: 2 possible outcomes with 3 systems gives 2^3 or 8 permutations.
Inserted Code
  1 2 3 4 5 6 7 8
A W W W W L L L L
B W W L L W L L W
C W L L W W W L L

I pasted this into an Excel sheet and inserted the probabilities for W as 0.6 and L as 0.4 to the right of the letter. The 3 systems (ABC) are listed in rows down the left and the different combinations are listed from 1 to 8 across the top. As you can see, the probability of all winning at once is 0.216 (0.6^3) and all losing at once is 0.064 (0.4^3) as you computed.
Attached Image

The probability of the majority (2 or more out of 3) of systems simultaneously winning sums up to 0.648 (highlighted in yellow). Doing it this way (via a table) gets complicated fast if you have a large number of systems to simulate. Bear in mind that these are ideal (maximum) numbers and it is likely that due to imperfections in correlation, system combinations may not perform this well in practice.
Attached File(s)
File Type: xlsx PipPirates_3Sys_Probability.xlsx   10 KB | 281 downloads
  • #3
  • Last Post: Jul 12, 2015 11:24pm Jul 12, 2015 11:24pm
Quoting FXEZ
Hi PipPirates. Your assumption that the 3 systems are independent is important for this math to work out. This implies that the 3 systems have zero correlation to each other. Let's just work out all the 3 system possibilities: 2 possible outcomes with 3 systems gives 2^3 or 8 permutations. 1 2 3 4 5 6 7 8 A W W W W L L L L B W W L L W L L W C W L L W W W L L I pasted this into an Excel sheet and inserted the probabilities for W as 0.6 and L as 0.4 to the right of the letter. The 3 systems (ABC) are listed in rows down the left and the different...
Thank you FXEZ for your time for making excel sheet. Its really helpful.
Thank you very much!
Actually I was calculating this for binary option trade, where three system means 3 currencies. Testing 3 currencies performance all together with one system.
Discussion is an exchange of knowledge;argument is an exchange of ignorance
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