Independent or not

You will write a test for independence, a function for the probability that at least one of several independent events happens, and a test for mutual independence of three events. The checker uses two dice and three coins.

The idea. Events $A$ and $B$ are independent when $P(A \cap B) = P(A)\,P(B)$. For independent chances $p_1, p_2, \dots$, the probability that none happens is the product of the $(1 - p_i)$. Three events are mutually independent when every pair passes and the triple product also holds.

Your tasks.

1. Finish independent(a, b, space). Return True when the probability of both equals the product of the two probabilities.
2. Finish at_least_one(chances). Return the probability that at least one of the independent events with these chances happens.
3. Finish mutually_independent(a, b, c, space). Return True only when the three pairs and the triple all pass the product rule.