Strategies and Hints

1. The number of paths from (0, 0) to (4, 4) is = 70.

2. The number of paths from (0, 0) to (2, 2) is = 6. The number of paths from (2, 2) to
   (4, 4) is the same: = 6. The product 6 x 6 represents the number of possible paths from (0, 0) to (4, 4) that pass through (2, 2).

3. Since the marker can move to just two different places, tossing a coin would be one way to randomly determine each move. One possible definition of winning is that the person whose marker lands at (4, 4) first wins.

Solution

The probability of passing through (2, 2) is ÷ or .