One-hundred students attend a statistics lecture. For the exam, students have two practice exams available. Fifty per cent of the students complete practice exam #1. Fifteen percent complete practice exam #1, but not practice exam #2. Twenty percent complete practice exam #2 but not practice exam #1. Student A is picked at random. Student A indicates that he/she completed practice exam #1. B indicates that he/she completed practice exam #2.

1. Using the appropriate logical operators between A and B, represent the following events and determine the probability that the student completed.

(a) No practice exam,

(b) Exactly one practice exam,

(c) Both practice exams,

(d) At least one practice exam,

(e) At least one practice exam.

2. Are the events stochastically independent? Explain your answer.

3. The student has completed practice exam #1. What is the probability that he also completed practice exam #2?