your teacher has invented a fair dice game to play. 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.

Question

your teacher has invented a fair dice game to play. 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.
 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).

Reiny · Answer

Consider the outcomes as ordered pairs of the form
(teacher, student)

we could list them as follows

11 12 13 14 15 16
21 22 23 24 25 26
...
71 72 73 74 75 76
81 82 83 84 85 86

there are 48 outcomes
15 have teacher < student
6 have teacher = student
27 have teacher > student

P(teacher wins) = 27/48 = 9/16