180 students in a tenth grade high school class take a survey about which video game consoles they own.
80 students answer that one of their consoles is a Playstation, 90 answer that one of their consoles is an
Xbox. Out of these, there are 30 who have both systems.

Let A be the event that a randomly selected student in the class has a Playstation and B be the event that
the student has an Xbox. Based on this information, answer the following questions.

What is P(A), the probability that a randomly selected student has a Playstation?

What is P(B), the probability that a randomly selected student has an Xbox?

What is P(A and B), the probability that a randomly selected student has a Playstation and an Xbox?

What is P(B A), the conditional probability that a randomly selected student has an Xbox given that he or she has a Playstation?

Is P(B|A) = P(B)? Are the events A and B independent?