The ant is moving through the coordinate system, Started at $(0,0)$ to $(4,4)$. What is the probability that the ant will find food at $(3,2)$?

Question

The path to the $(3,2)$ is $3+2 \choose 3$ or $3+2 \choose 2$.

Total path is $4+4 \choose 4$

And the probability is : $ \frac{3+2 \choose 3}{4+4 \choose 4}$ =

$ \frac{5 \choose 3}{8 \choose 4}$ = $\frac{10}{70}$ = $0.14$

I am not sure if I solved this problem corectly.

Answer 1

It is not correct. Note that there are $\binom{3}{1}$ ways from $(3,2)$ to $(4,4)$.