The following problem is from the semifinals of the Federation Francaise des Jeux Mathematiques:
One draws randomly an infinite sequence with digits 0, 1 or 2. Afterwards, one reads it in the order of the drawing.
What is the probability that one reads "2,0,1,2" without having read "0,1,2" beforehand?
Besides the obvious assumption that digits are drawn independently with equidistribution, I am primarily interested in the following interpretation:
*) If the sequence starts with 0,1,2,0,1,2 one regards this as having read 0,1,2 before 2,0,1,2 because the first pattern is finished before the second.
In addition, I would also like a solution to the following alternative interpretation, especially if it turns out to be easier to calculate:
*) If the sequence starts with 0,1,2,0,1,2 one regards this as NOT read 0,1,2 before 2,0,1,2 at this point because the first pattern has not finished before the second starts.