Question

Suppose that E and F are two events and that P(E) = 0.3 and P(F/E) = 0.9What is P(E and F)?

Answer 1

Probability

We want to find P (E ∩ F)

We know that

`P(F|E)=(P(F\cap E))/(P(E))`

Multiplying P ( E ) both sides, we find the P (E ∩ F) equation:

`P(E)P(F|E)=P(F\cap E)`

Replacing P( E ) = 0.3 and P( F | E ) = 0.9, we find that

`\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}`

Answer: D. 0.27