1. A teacher wants to select randomly a student from a group of 4 students. The names of the students are Anna, Maria, Alex, Ivan.

(a) Define the set of basic outcomes for this problem. What is the probability of each outcome?

(b) Consider the random events A = "the name of the selected student starts with A", B = "the name of the selected student ends with a". What outcomes do they consist of? What are their probabilities?

(c) Find the probabilities of the events AB, AB, A\B, (notA)(not B), (not A)(not B).

Include Venn diagrams for each of 5 cases in(c); shade the areas in question.

2. Consider the same 4 students as in the previous problem, but suppose that the teacher wants to select 2 students.

(a) Define the set of basic outcomes for this problem (you can abbreviate the names to write less). What is the probability of each outcome?

(b) Let A = "the name of at least one of the selected student starts with A", B = "the name of at least one of the selected student endswith a". Find the probabilities of these events.

(c) Find the probabilities of the events AB, AB.