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This was on wiki, and kaplan blue book had a similar question with same answer.
The prior probability of each event describes how likely the outcome is before the dice are rolled, without any knowledge of the roll's outcome. For example, die 1 is equally likely to fall on each of its 6 sides, so P(A) = 1/6. Similarly P(B) = 1/6. Likewise, of the 6 × 6 = 36 possible ways that a pair of dice can land, just 5 result in a sum of 8 (namely 2 and 6, 3 and 5, 4 and 4, 5 and 3, and 6 and 2), so P(C) = 5/36.
Why isn't the answer 6/36, How come they don't count 4 and 4 twice, namely, the possible combinations should be 2&6, 3&5, 4&4, 4&4, 5&3, and 6&2 shouldnt it?
The prior probability of each event describes how likely the outcome is before the dice are rolled, without any knowledge of the roll's outcome. For example, die 1 is equally likely to fall on each of its 6 sides, so P(A) = 1/6. Similarly P(B) = 1/6. Likewise, of the 6 × 6 = 36 possible ways that a pair of dice can land, just 5 result in a sum of 8 (namely 2 and 6, 3 and 5, 4 and 4, 5 and 3, and 6 and 2), so P(C) = 5/36.
Why isn't the answer 6/36, How come they don't count 4 and 4 twice, namely, the possible combinations should be 2&6, 3&5, 4&4, 4&4, 5&3, and 6&2 shouldnt it?
