Let S = {1, 2, dots, 20}. A subset B of S is | vedclass

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(B) The sum of all elements in $S = \{1, 2, \dots, 20\}$ is given by $\frac{20 	imes 21}{2} = 210$. Let $B$ be a subset of $S$ such that the sum of i

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$\frac{5}{2^{20}}$

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(B) The sum of all elements in $S = \{1, 2, \dots, 20\}$ is given by $\frac{20 	imes 21}{2} = 210$. Let $B$ be a subset of $S$ such that the sum of its elements is $203$. Let $B^c = S \setminus B$ be the complement of $B$ in $S$. The sum of the elements of $B^c$ is equal to $(	ext{Sum of } S) - (	ext{Sum of } B) = 210 - 203 = 7$. We need to find the number of subsets of $S$ whose elements sum to $7$. The possible subsets of $S$ whose elements sum to $7$ are: $1. \{7\}$ $2. \{1, 6\}$ $3. \{2, 5\}$ $4. \{3, 4\}$ $5. \{1, 2, 4\}$ There are $5$ such subsets. The total number of subsets of $S$ is $2^{20}$. Therefore,the probability that a randomly chosen subset is "nice" is $\frac{5}{2^{20}}$.

Let $S = \{1, 2, \dots, 20\}$. $A$ subset $B$ of $S$ is said to be "nice" if the sum of the elements of $B$ is $203$. Then the probability that a randomly chosen subset of $S$ is "nice" is

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