Getting a sum of either 7 or 12 on a roll of two dice. overlapping or non overlapping? probability of combined events?

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.

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