JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Probability

Let

S = {1, 2, \dots, 20}

. A subset

B

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:

Answer: (B)

Solution

The elements of

S = {1, \dots, 20}

sum to

\frac{20 \cdot 21}{2} = 210

, so a subset

B

has sum

203

exactly when the elements left out sum to

7

. The subsets of

S

adding to

7

are

{7}

{1, 6}

{2, 5}

{3, 4}

and

{1, 2, 4}

— five of them. Against the

2^{20}

subsets in all, the probability is

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

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Single correct option