Refer to dice that are loaded so that the numbers 2, 4, and 6 are equally likely to appear. 1, 3, and 5 are also equally likely to appear, but 1 is three times as likely as 2 is to appear.

#1)Two dice are rolled. What is the probability of getting a sum of 6 or doubles given that at least one die shows 2?

To roll 6: 5/36

To roll doubles: 6/36

To have at least one 2: 11/36

(5/36)/(11/36) = 5/11

(6/36)/ (11/36) = 6/11

It this correct?

#2)Two dice are rolled. What is the probability of getting a sum of 6 or a sum of 8 given that at least one die shows 2?

To roll 6: 5/36

To roll 8: 5/36

To have at least one 2: 11/36

(5/36)/(11/36) = 5/11

(5/36)/ (11/36) = 5/11

It this correct?

Thank you.