The correct answers are:
Non-overlapping; and 7/36.
Explanation:
Non-overlapping events, or mutually exclusive events, are events that cannot happen at the same time. When we roll 2 dice, we cannot get a sum of 7 and a sum of 12 at the same time, so they are non-overlapping.
To find the probability of two non-overlapping events, P(A or B), we add the probabilities.
To get a sum of 7, we can roll a 1&6; 6&1; 2&5; 5&2; 3&4; or 4&3. This makes 6 ways out of 36 total to get a 7.
To get a sum of 12, we can roll a 6&6. This makes 1 way out of 36 to get a 12.
This makes 6/36+1/36 = 7/36.
