Calculate some probabilities.
I used integer percentages rather than decimals for my inputs.
Probably more time was spent thinking up a design than coding. My main motivation was to think through how I, as a human, would work through the example problem given (input/sample2).
The notation:
P(A)for the probability of an event happening.P(!A)for the probability of an event not happening.P(A & B)for the probability of both events happening.P(A + B)for the probability of at least one event happening (notP(A | B)for the potential to confusion with conditional probability, though conditional probability is not discussed here).
The thought process:
- Given that
P(!A & !B & !C) = 0.1, I would knowP(A + B + C) = 1.0 - 0.1 = 0.9 - Given that
P(A & !B & !C) = 0.13and the above inference, I would knowP(B + C) = 0.9 - 0.13 = 0.77. P(B + C) = P(B) + P(C) - P(B & C), meaning0.77 = 0.7 + 0.27 - P(B & C)
The useful part was to see that when we learn about P(E) and know about P(E') where E is a subset of E', we can infer P(E' - E) or P(E' & !E).
This is the general case of "When we learn P(E), we can infer P(!E)" - the specific case here is where E' = S.
Similarly, when we learn P(E) and know about a P(E') that is mutually exclusive with E, we can infer P(E + E').
The rule about P(B + C) = P(B) + P(C) - P(B & C) did not need to be specifically implemented.