On a lottery ticket are four squares. You scratch the square to reveiw what is marked on it. On one of the square is marked "Loser". "Winner" is marked on two of the other three squares. You win by getting two "Winner"s before scratching the "Loser".

1. What is the probability of winning the ticket?
2. Will the probability of winning go up or down if there are six squares on the ticket while the rule of winning remains the same?

The probability of winning is not affected by the number of blank squares on the ticket. Blank squares are neutral to the rule of winning. The problem can be reduced to not getting the "Loser" out of three squares.

The chance of not getting the "Loser" in the first scratch is 2/3 and that in the second scratch is 1/2. The probability of winning the ticket is therefore

           2/3 * 1/2 = 1/3