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 .
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}.
Statement -1 is true, statement -2 is true ; statement -2 is a correct explanation of statement-1.
Statement -1 is true, statement -2 is true ; statement -2 is not a correct explanation of statement-1.
Statement -1 is true, statement -2 is false.
Statement -1 is false, statement -2 is true.
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
- 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
It cann't be
Total outcomes
Favourable sets (with all differences)
Probability
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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