1,1

Newsgroup article Probabilityquestion of sci.math, Mar 6 2006.

Example a(n=1)=4: after first throw, probability of the

face k is 1/6, 5/6 against. After 2nd throw, probability

of face k not shown before but at the 2nd throw is (5/6)*(1/6).

After 3rd throw, probability of face k only at this throw is (5/6)^2*(1/6),

but total probability 1/6+(5/6)*(1/6)+(5/6)^2*(1/6) still less than 0.5.

After the 4th throw, total probability is

1/6+(5/6)*(1/6)+(5/6)^2*(1/6)+(5/6)^3*(1/6) > 0.5.

with(linalg) : # Markov state approach with probability transition matrix trans # and n+1 different states for n from 1 to 30 do trans := array(1..n+1, 1..n+1) : for co from 1 to n do trans[1, co] := 5/6 ; for ro from 2 to n +1 do trans[ro, co] := 0 ; od ; trans[co+1, co] := 1/6 : od: # initial state: a previous 4-series for ro from 1 to n do trans[ro, n+1] := 0 : od : trans[n+1, n+1] := 1 : istate := vector(n+1) : istate[1] := 1 : for ro from 2 to n+1 do istate[ro] := 0 : od : #throw die with initial state vector istate for thro from 1 do istate := multiply(trans, istate) : if ( istate[n+1] > 1/2 ) then print(n, thro) ; break ; fi ; od : od:

Sequence in context: A123351 A119697 A132849 this_sequence A057416 A089154 A113450

Adjacent sequences: A115864 A115865 A115866 this_sequence A115868 A115869 A115870

more,nonn

R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 14 2006