Question

Assertion :Statement-1 : If A and B be mutually exclusive events in a sample space such that P(A) $=0.3andP\left(B\right)=0.6,$ then $p(\overline{A}\cap \overline{B})=0.28$ Reason: Statement-2 : If A and B are mutually exclusive events then $P(A\cap B)=0$

• A. Statement-1 is true, statement-2 is true ;
  statement-2 is not a correct explanation for
  statement-1
• B. Statement-1 is true, statement-2 is false
• C. Statement-1 is false, statement-2 is true
• D. Statement-1 is true, statement-2 is true ;
  statement-1 is a correct explanation for
  statement-1

Answer 1

The correct option is C Statement-1 is false, statement-2 is true

Since A and B be mutually exclusive events in a sample space $P(A\cap B)$=0

P(A)=0.3 P(B)=0.6

=0.3andP(B)=0.6

$P(\stackrel{\_}{A}\cap \stackrel{\_}{B})$= 1-P(AUB)

= 1- (P(A)+P(B)-$P(A\cap B)$)

=1- (0.3+0.6-0)

=0.1

If A and B are mutually exclusive events then P(A∩B) is always 0