Directions : Question are Assertion- Reason type questions. Each of these questions contains two statements. Statement-1 (Assertion) and Statement-2 (Reason). Each of these questions also has four alternative choices,only one of which is the correct answer. You have to select the correct choice:

Question: Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ..., 20}.

Statement-1 : The probability that the chosen numbers when arranged in some order will form an A.P. is \frac{1}{85}  .

Statement-2 : If the four chosen numbers form an A.P., then the set of all possible values of common difference is {±1, ±2, ±3, ±4, ±5}.

 

 

 

 

 

 

  • Option 1)

    Statement -1 is true, statement -2 is true ; statement -2 is a correct explanation of statement-1.

  • Option 2)

    Statement -1 is true, statement -2 is true ; statement -2 is not a correct explanation of statement-1.

  • Option 3)

    Statement -1 is true, statement -2 is false.

  • Option 4)

    Statement -1 is false, statement -2 is true.

 

Answers (1)

As we learnt in 

 

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.

 

 If 4 numbers are chosen for an AP.

Out of {1, 2,3,  ----------- , 20}

Common differences can be \pm 1, \pm 2, \pm 3, \pm 4

It cann't be \pm 5

Total outcomes =\ ^{20}C_{4}=4845

Favourable sets \Rightarrow 57 (with all differences)

Probability =\frac{57}{4845}=\frac{1}{85}

 


Option 1)

Statement -1 is true, statement -2 is true ; statement -2 is a correct explanation of statement-1.

Incorrect

Option 2)

Statement -1 is true, statement -2 is true ; statement -2 is not a correct explanation of statement-1.

Incorrect

Option 3)

Statement -1 is true, statement -2 is false.

Correct

Option 4)

Statement -1 is false, statement -2 is true.

Incorrect

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