Answer:
[tex]P_{bottom}=\frac{1}{4}=0.25[/tex]
Step-by-step explanation:
Starting from the top, the ant can only take four different directions, all of them going down, every direction has a probability of 1/4. For the second step, regardless of what direction the ant walked, it has 4 directions: going back (or up), to the sides (left or right) and down. If the probability of the first step is 1/4 for each direction and once the ant has moved one step, there are 4 directions with the same probability (1/4 again), the probability of taking a specific path is the multiplication of the probability of these two steps:
[tex]P_{2steps}=\frac{1}{4}*\frac{1}{4}=\frac{1}{16}[/tex]
There are only 4 roads that can take the ant to the bottom in 2 steps, each road with a probability of 1/16, adding the probability of these 4 roads:
[tex]P_{bottom}=\frac{1}{16}+\frac{1}{16}+\frac{1}{16}+\frac{1}{16}=\frac{4}{16}=\frac{1}{4}[/tex]
The probability of the ant ending up at the bottom is [tex]\frac{1}{4}[/tex] or 0.25.
