A certain box has 13 cards and each card has one of the integers from 1 to 13 inclusive. Each card has a different number. If 2 different cards are selected at random, what is the probability that the sum of the numbers written on the 2 cards is less than the average (arithmetic mean) of all the numbers written on the 13 cards?  Pick:
A) 1/7  B) 1/13  C) 1/15  D) 1/22  E) 1/26
The average of the numbers is 7   The total number of ways to choose 2 cards from 13 cards is 13C2 = 78.   The ways to choose 2 cards with a sum less than the average are:   {1,2},{1,3},{1,4},{1,5},{2,3},{2,4}   The probability is 6/78 = 1/13   The answer is 1/13.
<result>B</result>
A certain box has 13 cards and each card has one of the integers from 1 to 13 inclusive. Each card has a different number. If 2 different cards are selected at random, what is the probability that the sum of the numbers written on the 2 cards is less than the average (arithmetic mean) of all the numbers written on the 13 cards?