Mission Improbable

Calculate some probabilities.

Notes

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 (not P(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 know P(A + B + C) = 1.0 - 0.1 = 0.9
• Given that P(A & !B & !C) = 0.13 and the above inference, I would know P(B + C) = 0.9 - 0.13 = 0.77.
• P(B + C) = P(B) + P(C) - P(B & C), meaning 0.77 = 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.

Source

https://www.reddit.com/r/dailyprogrammer/comments/2vs1c6