We wish to do an experiment to determine if ants search for food using a random search or directed search method. To help design the experiment we first will run some simulations. In the experiment,

ants are placed inside a $50mm50mm$ box. They cannot climb the wall, but can escape through an opening of size $10mm$ in the wall. Repeated measurements of how far an ant travels in $1$ second

show an average speed of $2mm$ per second. Our simulation needs to determine the probability that an ant escapes the box in $600$ seconds $($hint: so your main iteration would look like for $t$ in

range $(600)$ : $)$ if their motion is indeed random. Assume the ant is always initially placed in the center of the box and simulate a simple random walk in $2$D on discrete time in this fashion: Have the ant

live on a discrete lattice. The ant takes $2mm$ to the left if a random number $u$ satisfies The ant moves $2mm$ to the right if the ant moves $2mm$ up if and $2$

$mm$ down if $0\mathrm{.}75u1\mathrm{.}0.u$ is distributed uniformly between $0$ and $1($hint: use np$.$ random. uniform $($ low$=0,$ high$=1)$ to generate it$).$ If a step would take the ant into a wall, repeat the step until it

is successful $($result is still one time$-$step$).$ With attempts $=n.$ linspace $(10,1000,19),$ run your main iteration under the loop for $M$ in attempts: and construct a dataframe with columns

for number of attempts $($i$.$e$.$ M$),$ number of escapes, and probability of escape for every M$.$ Your dataframe would eventually look something like this with $19$ rows and real values: