In 1.54Pathfinding, we consider the a path with fixed start and end points on a grid. The paths may move right and up on the grid only. Suppose we have points ˆ A = (a1, a2) ˆ B = (b1, b2) ˆ C = (c1, c2) ˆ D = (d1, d2) where a1 < b1 < c1 < d1 and a2 < b2 < c2 < d2. (a) Write an expression for the probability that a random path from A to D will pass through both B and C. (b) Write an expression for the probability that a random path from A to D will pass through B, but not C. (c) Write an expression for the probability that a random path from A to D will pass through neither B nor C. (d) Find the probability a path from (0, 0) passes through (9, 9), but not (5, 5) or (7, 7).

In 1.54Pathfinding, we consider the a path with fixed start and end points on a grid. The
paths may move right and up on the grid only. Suppose we have points
ˆ A = (a1, a2)
ˆ B = (b1, b2)
ˆ C = (c1, c2)
ˆ D = (d1, d2)
where a1 < b1 < c1 < d1 and a2 < b2 < c2 < d2.
(a) Write an expression for the probability that a random path from A to D will pass through
both B and C.
(b) Write an expression for the probability that a random path from A to D will pass through
B, but not C.
(c) Write an expression for the probability that a random path from A to D will pass through
neither B nor C.
(d) Find the probability a path from (0, 0) passes through (9, 9), but not (5, 5) or (7, 7).