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.
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