01-22-2021, 05:20 PM
Hello grib,
your adjusted probabilities are correct, but unless I misunderstood your description of your assignment of the probabilities the attribution to the pattern is wrong. The way I underrstood your description the correct attribution is:
P(00) = 31,6% (that you had right)
P(01) = p(01) = 25% (first decision, 25%, 75% invers event p(!01) )
P(02) = 75% * 25% = 18,8% (second decision, p(!01) * p(02))
P(03) = 75% * 75% * 25% = 14% (third decision, p(!01) * p(!02) * p(03))
P(04) = 75% * 75% * 75% * 25% = 10,5% (forth decision, p(!01) * p(!02) * p(!03) * p(04))
And for completeness sake:
P(00) = 75% * 75% * 75% * 75% = 31,6% (inveres of forth decision, p(!01) * p(!02) * p(!03) * p(!04))
The sum of these is 100% (ignoring rounding errors), so it is complete, as expected.
If you want 01, 02, 03 and 04 with 25% chance each and no pattern 00 after pattern 00 just played then you'd have to adjust the probabilities as follows:
p(01) = 25% (remains unchanged)
p(02) = 33,33333333%
p(03) = 50%
p(04) = 100%
That will also remove your previous "other 00" step.
With the formulas above you could also compute any other set of resulting probabilities
Kind regards,
Michael
your adjusted probabilities are correct, but unless I misunderstood your description of your assignment of the probabilities the attribution to the pattern is wrong. The way I underrstood your description the correct attribution is:
P(00) = 31,6% (that you had right)
P(01) = p(01) = 25% (first decision, 25%, 75% invers event p(!01) )
P(02) = 75% * 25% = 18,8% (second decision, p(!01) * p(02))
P(03) = 75% * 75% * 25% = 14% (third decision, p(!01) * p(!02) * p(03))
P(04) = 75% * 75% * 75% * 25% = 10,5% (forth decision, p(!01) * p(!02) * p(!03) * p(04))
And for completeness sake:
P(00) = 75% * 75% * 75% * 75% = 31,6% (inveres of forth decision, p(!01) * p(!02) * p(!03) * p(!04))
The sum of these is 100% (ignoring rounding errors), so it is complete, as expected.
If you want 01, 02, 03 and 04 with 25% chance each and no pattern 00 after pattern 00 just played then you'd have to adjust the probabilities as follows:
p(01) = 25% (remains unchanged)
p(02) = 33,33333333%
p(03) = 50%
p(04) = 100%
That will also remove your previous "other 00" step.
With the formulas above you could also compute any other set of resulting probabilities
Kind regards,
Michael