Estimating a probability by simulation

You will write three small functions: one that finds a relative frequency in a list of results, one that simulates an event many times, and one that finds the band of the law of large numbers.

The idea. A relative frequency is the number of times an event happened divided by the number of tries. A computer can try an event of probability $p$ by checking random.random() < p, which is true about a share $p$ of the time. In about $95$ runs out of $100$, the share lands within $2\sqrt{p(1-p)/n}$ of $p$.

Your tasks.

1. Finish relative_frequency(results, target). Count how many items of the list equal target, and divide by the length of the list.
2. Finish simulate(p, n). Try the event n times and return the number of successes.
3. Finish band(p, n). Return the half-width $2\sqrt{p(1-p)/n}$.