to compute problemhttps://math.stackexchange.com/questions/2759407/ on math stack exchange

prob_5q.c

#include <stdio.h>

const double student1_probs[5] = {0.3, 0.4, 0.9, 0.7, 0.1}; /* item i is P(student 1 has question i correct) */
const double student2_probs[5] = {0.4, 0.5, 0.2, 0.8, 0.1};

int main(void){
        double successes1[6]= {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
        double successes2[6]= {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
        unsigned int i, b,j;
        for (i=0; i < 32;i++){
                double p1 = 1.0;
                double p2 = 1.0;
                unsigned int oks=0;
                b=1; j=0;
                while (b != (1 <<5)){
                        if (i & b){
                                p1 *= student1_probs[j];
                                p2 *= student2_probs[j];
                                oks++;
                        } else {
                                p1 *= (1-student1_probs[j]);
                                p2 *= (1-student2_probs[j]);
                        }
                        b <<=1;
                        j++;
                } /* now total probability of that combo us determined*/
                successes1[oks] += p1;
                successes2[oks] += p2;
        }
        for (i=0; i< 6; i++){
                fprintf(stdout, "P student 1 has %u correct = %f\n", i, successes1[i]);
                fprintf(stdout, "P student 2 has %u correct = %f\n", i, successes2[i]);
        }
        double P_1_gt_2 = 0.0; /* the chance that 1 has more than 2 */
        double P_1_eq_2 = 0.0;
        double P_2_gt_1 = 0.0;
        unsigned int score1, score2;
        for (score1 = 0; score1 < 6; score1++){
                for (score2=0; score2 < 6; score2++){
                        if (score1 == score2){
                                P_1_eq_2 += successes1[score1] * successes2[score2];
                        } else if (score1 < score2){
                                P_2_gt_1 += successes1[score1] * successes2[score2];
                        } else {
                                P_1_gt_2 += successes1[score1] * successes2[score2];
                        }
                }
        }
        fprintf(stdout, "1 does better with probability %f\n", P_1_gt_2);
        fprintf(stdout, "2 does better with probability %f\n", P_2_gt_1);
        fprintf(stdout, "equal score with probability %f\n", P_1_eq_2);

        return 0;


}