$180$ 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? **[[☃ input-number 1]]
**What is $P(B)$, the probability that a randomly selected student has an Xbox? **[[☃ input-number 2]]
**What is $P(A\text{ and }B)$, the probability that a randomly selected student has a Playstation *and* an Xbox?** [[☃ input-number 3]]
**What is $P(B\text{ | }A)$, the conditional probability that a randomly selected student has an Xbox given that he or she has a Playstation?** [[☃ input-number 4]]
**Is $P(B\text{ | }A)=P(B)$?
Are the events $A$ and $B$ independent?** [[☃ radio 1]]