Your teacher has invented a “fair” dice game to play. Here’s how it works. Your teacher will roll one fair eight-sided die, and you will roll a fair six-sided die. Each player rolls once, and the winner is the person with the higher number. In case of a tie, neither player wins. The table shows the sample space of this chance process.

Teacher Rolls You Roll 1 2 3 4 5 6 7 8 1

2 3

4 5

6

(a) Let A be the event “your teacher wins.” Find P(A).

(b) Let B be the event “you get a 3 on your first roll.”

Find P(A ∪ B).

(c) Are events A and B independent? Justify your answer.