(B) We know that $P(A) = 1 - P(\bar{A})$.Given $P(\bar{A}) = 0.65$,so $P(A) = 1 - 0.65 = 0.35$.For mutually exclusive events,$P(A \cap B) = 0$.The add

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(B) We know that $P(A) = 1 - P(\bar{A})$.Given $P(\bar{A}) = 0.65$,so $P(A) = 1 - 0.65 = 0.35$.For mutually exclusive events,$P(A \cap B) = 0$.The addition rule for probability is $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Substituting the given values: $0.65 = 0.35 + p - 0$.Solving for $p$: $p = 0.65 - 0.35 = 0.30$.

Competitive Quantitative Aptitude Probability Probability

Medium

$A$ and $B$ are mutually exclusive events of an experiment. If $P(\text{not } A) = 0.65$,$P(A \cup B) = 0.65$,and $P(B) = p$,find the value of $p$.

A
$0.70$
B
$0.30$
C
$0.63$
D
$0.35$

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$A$ and $B$ are mutually exclusive events of an experiment. If $P(\text{not } A) = 0.65$,$P(A \cup B) = 0.65$,and $P(B) = p$,find the value of $p$.

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