Question

For the event “both balls are black,” which expression correctly applies the Multiplication Theorem?

Options

• \[P(E\cap F)=P(F\mid E)\div P(E)\]

• \[P(E\cap F)=P(E)\cdot P(F\mid E)\]

• \[P(E\cap F)=P(E)+P(F)\]

• \[P(E\cap F)=P(E)\cdot P(F)\]

Answer 1

“Both balls are black” means that \[E\] and \[F\] occur together. Because the balls are drawn without replacement, use the conditional factor \[P(F\mid E)\].