Let's say there are 10 teams: A-J.
Each team always participate in each of the game.
Only 1 team wins, others lose.
Probability of any team to win is unknown (different for each team) and to be calculated.
There were 3 games: Game1, Game2, Game3.
Team A lost Game1 and Game2 and won Game3.
What is the probability of the team A to win Game4?
Now, more complex second question: let's say probability to win is unknown, but known to change over time. How would this affect the answer?
Best Answer
If the probability is unknown in advance then the estimate after $3^{rd}$ game is:
$P(A) = \frac13$; and same for teams who won $1^{st}$ and $2^{nd}$ games (if not a single team won both, in which case it would be $\frac23$ for that)
For the rest $P(x) = 0$.
The $2^{nd}$ does not seem like a question, but is almost obvious, probabilities calculated will change initially, at least till we get a large sample of experiments (games in this case). In the beginning, As Andre said, estimates are almost useless because of low number of trials. These will get more meaning after every experiment.