Statement-1: 20 persons are sitting in a row. Two of these persons are selected at random. The probability that the two selected persons are not together is 0.9.
Statement-2: If $\overline{A}$ denotes the negation of an event A, then $P(\overline{A})=1-P(A).$
Answer & explanation
Correct answer: option 1
Clearly, statement-2 is true.
The number of ways of selecting 2 persons out of 20 persons sitting in a row is ${^{20}C}_2 (=190)$ and the number of ways in which two selected persons sit together is 19.
∴ Thus, if A denotes the event "Two selected persons sit together". Then, $P (A) =\frac{19}{190}=\frac{1}{10}$
∴ Required probability $= P(\overline{A})$
$=1-P(A) $ [Using statement -2]
$=1-\frac{1}{10}=\frac{9}{10}=0.9$