Question

Assertion :20 persons are sitting in a row. Two of these persons are not random. The probability that the two selected person are not together is 0.9. Reason: If $\overline{A}$ denotes the negative of an event A, then $P\left(A\right)=1-P\left(A\right)$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Clearly, statement-2 is true.
The number of ways of selecting $2$ person out of $20$ persons sitting in a row is ${}^{20}{C}_2(=190)$ and the number of ways in which two selected person sit together is $19$.
$\therefore$ Thus, if A denotes the event "Two selected person sit together'. Then,
$P\left(A\right)=\frac{19}{190}=\frac{1}{10}$
$\therefore$ Required probability $=P\left(\overline{A}\right)$
$=1-P\left(A\right)$ [Using statement -2]
$=1-\frac{1}{10}=\frac{9}{10}=0.9$