#include <iostream>
using namespace std;
 
int main() {
	int   max_opportunities = 8;  // Total number of chances to flip.
    float flip_chance = 0.2;      // Probability of flipping each opportunity.
    float probability_true = 1.0; // Starting probability of truth.
                                  // 1.0 is "definitely true" and 0.0 is 
                                  // "definitely false", but you can extend this
                                  // to situations where the initial value is not
                                  // certain (say, 0.8 = 80% probably true) and
                                  // it will work just as well.
    for (int opportunities = 0; opportunities < max_opportunities; ++opportunities)
    {
        probability_true = probability_true * (1 - flip_chance) + 
                           (1 - probability_true) * flip_chance;
    }
 
    cout << probability_true << endl;
}

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