There are 6 seats in a row. I pick one of them at random and sit in it. Then my friends picks a seat at random from the 5 that remain, and sits in that one. The other four seats remain empty. Seats 1 and 6 will be called the "end seats." Let A denote the event that I sit in an end seat, and let B denote the event that my friend sits in an end seat.

a) Are A and B independent? Why or why not?

b) Are A and B mutually exclusive? Why or why not?

c) What is the chance that we both sit in an end seat? In other words, what is P(A and B)?

d) What is the chance that my friend and I sit next to each other?