If A and B are independent events such that \( P(A)=\displaystyle\frac{1}{2},\ P(A\cup B)=\frac{3}{5} \) and \( P(B)=p \), then value of p is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{1}{5} \)
For independent events \( P(A\cap B)=P(A)P(B) \), so the addition theorem gives
\( \displaystyle P(A\cup B)=P(A)+P(B)-P(A)P(B) \)
With the given values,
\( \displaystyle \frac{3}{5}=\frac{1}{2}+p-\frac{p}{2} \)
\( \displaystyle \frac{p}{2}=\frac{3}{5}-\frac{1}{2} \)
\( \displaystyle p=\frac{1}{5} \)
NCERT (2026-27 edition):
Independent Events
