Suppose that $$ E $$ and $$ F $$ are two events and that $$ P(E $$ and $$ F)=0.4 $$ and $$ P(E)=0.5 $$. What is $$ P(F \mid E) $$ ? $$ P(F \mid E)=\square $$ (Type an integer or a decimal.)

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1. The formula for the conditional probability is:
   $$
   P(F \mid E) = \frac{P(E \text{ and } F)}{P(E)}
   $$
2. Substitute the given values into the formula:
   $$
   P(F \mid E) = \frac{0.4}{0.5}
   $$
3. Simplify the fraction:
   $$
   P(F \mid E) = 0.8
   $$
$$ P(F \mid E) = 0.8 $$

Suppose that and are two events and that and and . What is ?
(Type an integer or a decimal.)

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Suppose that and are two events and that and and . What is ? (Type an integer or a decimal.)