A fair 6 sided die is rolled 6 independent times. Let Ai be the event that side i is observed on the i\'th roll, called a match on the i\'th trial, i = 1, 2, 3, 4, 5, 6. If we let B denote the event that at least one match occurs, find P(B). Solution p(B) = 1-(5/6)^6 =0.665.

1. A fair 6 sided die is rolled 6 independent times. Let Ai be the event that side i is observed on the
i'th roll, called a match on the i'th trial, i = 1, 2, 3, 4, 5, 6. If we let B denote the event that at
least one match occurs, find P(B).
Solution
p(B) = 1-(5/6)^6 =0.665