The probability that student Gromov will pass the criminal law exam is 0.7, and the probability of his passing

The probability that student Gromov will pass the criminal law exam is 0.7, and the probability of his passing the civil law exam is 0.8. What is the likelihood that he will successfully pass: a) both exams? b) at least one exam?

Probability to pass the criminal law exam: p1 = 0.7; the probability to fail is q1 = 1 – p1 = 1 – 0.7 = 0.3;
Probability to pass the civil law exam: p1 = 0.8; the probability to fail is q2 = 1 – p2 = 1 – 0.8 = 0.2;
a) The likelihood that a student will pass both exams:
P (2) = p1 p2 = 0.7 0.8 = 0.56.
b) The likelihood that a student will fail both exams:
P (0) = q1 q2 = 0.3 0.2 = 0.06.
The probability that a student will pass at least one exam:
P` (0) = 1 – P (0) = 1 – 0.06 = 0.94.
Answer: The probability that a student will pass at least one exam is 0.94.