Probability by listing the outcomes

You will write three small functions: one that finds a probability by counting outcomes, one that finds $P(A \cup B)$ with the addition theorem, and one that finds the probability of exactly one of two events. The checker uses two dice.

The idea. For equally likely outcomes, $P(E)$ is the number of outcomes in $E$ divided by the number of outcomes in the space. Use Fraction, so the answers stay exact. The addition theorem says $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.

Your tasks.

1. Finish prob(event, space). Return the fraction of outcomes of space for which event(o) is true.
2. Finish p_union(a, b, space). Use the addition theorem with the function from task 1.
3. Finish p_exactly_one(a, b, space). Use $P(A) + P(B) - 2P(A \cap B)$.