Given that the events A and B are mutually exclusive such that \( P(A)=\displaystyle\frac{1}{2} \) ,\( P(A\cup B)=\displaystyle\frac{2}{3} \) and \( P(B)=p \) , then the value of \( p \) is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{1}{6} \)
For mutually exclusive events, \( P(A\cap B)=0 \), so \( P(A\cup B)=P(A)+P(B) \).
\( \displaystyle \frac{2}{3}=\frac{1}{2}+p \)
\( \displaystyle p=\frac{2}{3}-\frac{1}{2}=\frac{1}{6} \)