JEE PYQ: Probability Question 46
Question 46 - 2019 (11 Jan Shift 2)
Let $S = {1, 2, \ldots, 20}$. 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:
(1) $\frac{7}{2^{20}}$
(2) $\frac{5}{2^{20}}$
(3) $\frac{4}{2^{20}}$
(4) $\frac{6}{2^{20}}$
Show Answer
Answer: (2)
Solution
Sum of all elements $= \frac{20 \times 21}{2} = 210$. Need subsets with sum $= 203 = 210 - 7$. Complement has sum 7. Subsets of ${1,…,20}$ with sum 7: ${7}, {1,6}, {2,5}, {3,4}, {1,2,4}$ = 5 subsets. $P = \frac{5}{2^{20}}$.
BETA
