A binomial experiment by simulation

You will simulate many repeats of a binomial experiment with a fixed seed, turn the counts into shares, and check that they match the formula. The checker uses classes of $10$ students who each cycle with probability $0.3$.

The idea. One repeat counts the successes in n trials, where a trial succeeds when rng.random() < p. Many repeats give a list of counts. The share of count k is how often k appears, divided by the number of repeats.

Your tasks.

1. Finish one_count(rng, n, p).
2. Finish simulate(n, p, repeats, seed). Make rng = random.Random(seed) and return the list of counts.
3. Finish shares(counts, n). Return a list of $n + 1$ shares, for the counts $0$ to $n$.