The probabilities of successful passing of the exam in the first, second and third subject for this student

The probabilities of successful passing of the exam in the first, second and third subject for this student are equal to 0.6; 0.7; 0.8. Find the probability that he: a) will pass all the exams; b) fails at least one exam; c) will pass only the first exam

1) Probability of successfully passing all three exams:

P = P1 * P2 * P3, where P1 = 0.6; P2 = 0.7; P3 = 0.8.

P = 0.6 * 0.7 * 0.8 = 0.336.

2) Probability of not passing at least one exam:

P = 1 – P1,2,3 = 1 – 0.336 = 0.664.

3) Probability to pass only the first exam (the second and third are not passed):

P = P1 * q2 * q3, where q2 is the probability of not passing the second exam (q2 = 1 – P2 = 1 – 0.7 = 0.3), q3 is the probability of not passing the third exam (q3 = 1 – P3 = 1 – 0.8 = 0.2).

P1 = P1 * q2 * q3 = 0.6 * 0.3 * 0.2 = 0.036.