The set S consists of 5 numbers: {1,2,3,4,5}. If all possible subsets including the null set are created and one subset is chosen at random, what is the probability that the subset has 3 or 4 as its largest number? Choose one:  A) 3/4  B) 3/8  C) 3/16  D) 5/16  E) 3/32
The set S has 2^5 = 32 subsets.   The number 5 is in half of these subsets.   Of the remaining 16 subsets, 4 is an element in 8 of them.   Thus 4 is the largest number in 8 subsets of S.   Of the remaining 8 subsets, 3 is an element in 4 of them.   Thus 3 is the largest number in 4 subsets of S.   The probability that 3 or 4 is the largest number is 12/32 = 3/8.   The answer is C.
<result>B</result>
The set S consists of 5 numbers: {1,2,3,4,5}. If all possible subsets including the null set are created and one subset is chosen at random, what is the probability that the subset has 3 or 4 as its largest number?