Problem 2. The probability of a student passing the credit is 0.8. If the credit is passed, the student is allowed to take the exam, the probability of passing which is 0.9. Find the probability that the student will pass the credit and the exam.
Solution. Let's denote the events: $A$ - passing the test, $B$ - passing the exam. Then $A B$ means that the student passes both the test and the exam. Event $B$ depends on event $A$, so $p(A)=0.8, p(B / A)=0.9$. By formula (9) we have $p(A B)=0.8 \cdot 0.9=0.72$.