The binomial by code

You will write the binomial probability, a cumulative probability and a search for the number of trials needed to reach a target chance. The checker uses exact fractions.

The idea. For $n$ trials with success probability $p$, $P(X = k) = \binom{n}{k}p^k(1 - p)^{n-k}$. "At most $k$" adds the terms from $0$ to $k$. To reach a target chance of at least one success, increase $n$ until $1 - (1 - p)^n$ is at least the target.

Your tasks.

1. Finish binomial(n, p, k). Use comb(n, k) from the math module.
2. Finish at_most(n, p, k). Add binomial(n, p, j) for j from $0$ to k.
3. Finish smallest_n(p, target). Return the smallest n for which the chance of at least one success is at least target.