Posted by Koia on Thursday, May 10, 2012 at 3:23am.
The geometric distribution gives the probability of getting a success at the xth trial:
P(X=x)=Px(x)=(1-p)^(x-1)p
The probability of getting the first success in n trials is therefore the sum of the above, or
P(n)=Σ(1-p)^(n-1)p
=pΣ(1-p)^(n-1) (geom seq.)
=p(1-(1-p)^n)/p
=1-(1-p)^n
So
P(1)=1/6
P(2)=11/36
...
P(5)=4651/7776=0.598
P(10)=50700551/60466176=0.838
P(13)=11839990891/13060694016=0.906
P(15)=439667406451/470184984576=0.939
...
it really make me confusing what you are mention, how could i describe what you did
If you have not done the geometric distribution at school, you need to read up about it before. I agree that it is not obvious if you have not done the distribution before, or if you have not done summation of geometric series before.
In my calculations above,
P(1) is the probability of obtaining at least one favourable outcome with one trial (throw of die)
P(2) is the probability of obtaining at least one favourable outcome (throwing a six) with 2 trials.
...
P(n) is the probability of obtaining at least one favourable outcome with n throws of the die.
It turns out that with 13 throws, the probability of getting at least "six" once is 0.9, as shown above.