T5.11. 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...

Extracted text: T5.11. 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 3 4 5 6 7 8 1 2 3 4 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 U B). (c) Are events A and B independent? Justify your answer.