Practicing Success
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 $P(\overline{A})=1-P(A).$ |
Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for Statement 1. Statement 1 is True, Statement 2 is True; Statement 2 is not a correct explanation for Statement 1. Statement 1 is True, Statement 2 is False. Statement 1 is False, Statement 2 is True. |
Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for Statement 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] $=1-\frac{1}{10}=\frac{9}{10}=0.9$ |