Probability
We want to find P (E ∩ F)
We know that
[tex]P(F|E)=\frac{P(F\cap E)}{P(E)}[/tex]
Multiplying P ( E ) both sides, we find the P (E ∩ F) equation:
[tex]P(E)P(F|E)=P(F\cap E)[/tex]
Replacing P( E ) = 0.3 and P( F | E ) = 0.9, we find that
[tex]\begin{gathered} P(F\cap E)=P(E)P(F|E) \\ P(F\cap E)=0.3\cdot0.9 \\ P(F\cap E)=0.27 \end{gathered}[/tex]
Answer: D. 0.27
