Question

Let S = {1, 2,....., 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)  4/2²⁰

(2)  7/2²⁰

(3)   5/2²⁰

(4)  6/2²⁰

Answer 1

Correct option  (3)  5/2²⁰

Explanation:

Sum of all number of set S = 210.

We have to find numbers whose sum is 203.

So basically we have to remove 7.

7 can be obtained as 7

1, 6

2, 5

3, 4

1, 2, 4 

Total = 5

Samples space = 2²⁰ 

So   5/2²⁰.