Question

If \(P(E)=\dfrac{3}{7},\ P(F)=\dfrac{5}{7},\ P(E\cup F)=\dfrac{6}{7}\), then \(P(E\cap F)=\) ?

• A. \(\dfrac{4}{7}\)
• B. \(\dfrac{2}{7}\)
• C. \(\dfrac{1}{7}\)
• D. \(\dfrac{3}{7}\)

Hint:

Union \(=\) sum minus overlap: \(P(E\cup F)=P(E)+P(F)-P(E\cap F)\).

Answer 1

The Correct Option is B

Reason. Use the addition law: \[ P(E\cup F)=P(E)+P(F)-P(E\cap F). \] Compute: \[ \frac{6}{7}=\frac{3}{7}+\frac{5}{7}-P(E\cap F) \ \Rightarrow\ P(E\cap F)=\frac{3+5-6}{7}=\frac{2}{7}. \]