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  • Confused! kindly explain, 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:

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: 

  • Option 1)    (7/220)
  • Option 2) (4/220)  
  • Option 3)(5/220) 
  • Option 4) (6/220) 

Answers (1)

best_answer

 

Probability of occurrence of an event -

Let S be the sample space then the probability of occurrence of an event E is denoted by P(E) and it is defined as 

P\left ( E \right )=\frac{n\left ( E \right )}{n\left ( S \right )}

P\left ( E \right )\leq 1

P(E)=\lim_{n\rightarrow\infty}\left(\frac{r}{n} \right )

- wherein

Where n repeated experiment and E occurs r times.

S_{Total}=1+2+3.......................+20

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

S_{Total}-S_{nice}=7

Possibilities of numbers that can be removed from S_{Total}\: \: to \: \:become\: \: S_{nice}

(7), (1,6) , (2,5) , (3,4) , (1,2,4)

=>p=\frac{5}{2^{20}}

 

 

 

 


Option 1)

\frac{7}{2^{20}}

Option 2)

\frac{4}{2^{20}}

Option 3)

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

Option 4)

\frac{6}{2^{20}}

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