#include <iostream>

// calculates the probability of the events A or B for independent events

double addition_rule_independent(double A, double B) {
    return (A + B) - (A * B);
}

// calculates the probability of the events A or B for dependent events
// note that if value of B_given_A is unknown, use chainrule to find it

double addition_rule_dependent(double A, double B, double B_given_A) {
    return (A + B) - (A * B_given_A);
}

int main() {
    double A = 0.5;
    double B = 0.25;
    double B_given_A = 0.05;

    std::cout << "independent P(A or B) = "
    << addition_rule_independent(A, B) << std::endl;

    std::cout << "dependent P(A or B) = "
    << addition_rule_dependent(A, B, B_given_A) << std::endl;

    return 0;
}