probability and statistics

Question

If a pair of standard dice are rolled, what is the probability that at least one die shows a 5? Be sure to reduce the answer.

Answer 1

there are different approaches

there are 36 outcomes when you roll two dice

you want at least one 5

the possibilities are...

(1,5), (2,5), (3,5), (4,5), (5,5), (6,5), (5,1), (5,2), (5,3), (5,4), (5,6)

there are 11 ways to get at least one 5 out of a total of 36 combinations

the answer is 11/36

another way is the probability of 5 and then no 5 is (1/6)(5/6)=5/36

the probability of no 5 and then 5 is (5/6)(1/6)=5/36

the probability of 5 and then 5 again is (1/6)(1/6)=1/36

5/36 + 5/36 + 1/36=11/36

another way: 1-(probability of no 5's at all)

probability of no 5's at all is (no 5) times (no 5)

(5/6)(5/6)=25/36

1-25/36=36/36-25/36=11/36