SOLUTION: A pair of fair dice is thrown. If the two numbers appearing are different, find the probability that a) the sum is 6 b) the sum is 4 or less.

In all, there are 36 possible different outcomes.

Of them, 6 outcomes are pairs with equal appearing, and the rest 30 pairs are with different appearing.

For our conditional probability problem, these 30 pairs comprise our reduced space of events.



The sum of 6 produce these five pairs (1,5), (2,4), (3,3), (4,2), (5,1).

Of these 5 pairs, we exclude the pair (3,3), since this pair is of equal appearance.

Thus the number of favorable pairs in our problem is 4.



The probability under the problem's question is  

    P =  =  = .         ANSWER