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Aren't $A$ and $B$ Mutually exclusive? SO why isn't the answer just

$P(A \cup B) = P(A) + P(B)$

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    Why couldn't you roll a 6 on both rolls? – 2017-01-20
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    Events arent mutually exclusive if they have an element in common. But I don't see why this isnt mutually exclusive @ZacharySelk – 2017-01-20
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    Mutually exclusive means that if one happens then the other can't happen. So if you roll a 6 on the first, why couldn't you roll a 6 on the second? – 2017-01-20
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    You can though @ZacharySelk . So is that why these arent mutually exclsuive? – 2017-01-20
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    They aren't mutually exclusive, yes. – 2017-01-20

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Sample space

 11  12  13  14  15  16
 21  22  23  24  25  26
 31  32  33  34  35  36
 41  42  43  44  45  46
 51  52  53  54  55  56
 61  62  63  64  65  66

Event $A$ consists of the 6 points in the last row. Event $B$ consists of the 6 points in the last column. Event $A\cap B$ consists of the single point 66; this is an event 'in common'. So $A$ and $B$ are not mutually exclusive (disjoint).

However, $A$ and $B$ are independent because $P(A\cap B) = P(A)P(B).$ If I am told that a 6 occurred on the first roll, that tells me nothing about my chances of getting a 6 again on the second roll.

As you begin to study probability, it is important that you not confuse the concepts of disjointness and independence.

  • Disjointness is a logical concept. In a draw from a deck of cards, I can tell you that Hearts and Spades are disjoint without knowing anything about whether the draw is 'fair'.

  • But I can't begin to discuss whether two events are independent, unless I know about the probability structure. If I know that I'm drawing 'at random' from a full standard deck of 52 cards, then I know that Ace and Heart are independent events.