Question

For any event A, if P(A) = 0.25,find P(not A). (A) 0 (B) 1 (C) 0.25 (D)0.75
Give explanation..

Answer 1

P(A) + P(not A) = 1 and hence P(not A) = 0.75

Answer 2

$\underline{\blue{ Complementary \: event: }}$

$The \: event \: which \:is \: against \:to \\occuring \: to \: 'A' \: is \: called \:as \\complementary \:event . It \: is \: denoted \: by \: \bar {A} .$

$\pink{The \: sum \: of \: Probability \:of }\\\pink{ occuring \: 'A' \:and \: probability \: of \: not}\\\pink{ occuring \: 'A' = 1 }$

$Here, P(A) = 0.25$

$\boxed{ \green {P(A) + P( not \: A ) = 1}}$

$\implies 0.25 + P( not \: A ) = 1$

$\implies P(not \: A ) = 1 - 0.25$

$\implies P(not \: A ) = 0.75$

Therefore.,

$Option \: \green { ( D ) } \:is \: correct.$

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