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)`.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Answer

A

Explanation

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 in which two selected persons sit together is 19.
Thus, if A denotes the event " two selectd persons sit together " then , P (A) =` 19/190 = 10`
Required probability = =` P ( overline (A))`
1- P (A) [ Using satement -2]
`1- 1/10 = 9/10 = 0.9`