Question:
If \(P(E)=\dfrac{3}{7},\ P(F)=\dfrac{5}{7},\ P(E\cup F)=\dfrac{6}{7}\), then \(P(E\cap F)=\) ?
If \(P(E)=\dfrac{3}{7},\ P(F)=\dfrac{5}{7},\ P(E\cup F)=\dfrac{6}{7}\), then \(P(E\cap F)=\) ?
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Union \(=\) sum minus overlap: \(P(E\cup F)=P(E)+P(F)-P(E\cap F)\).
Updated On: Oct 17, 2025
- \(\dfrac{4}{7}\)
- \(\dfrac{2}{7}\)
- \(\dfrac{1}{7}\)
- \(\dfrac{3}{7}\)
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The Correct Option is B
Solution and Explanation
Reason. Use the addition law:
\[
P(E\cup F)=P(E)+P(F)-P(E\cap F).
\]
Compute:
\[
\frac{6}{7}=\frac{3}{7}+\frac{5}{7}-P(E\cap F)
\ \Rightarrow\ P(E\cap F)=\frac{3+5-6}{7}=\frac{2}{7}.
\]
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