Question

What conclusion can be drawn from the following statements? P(E|F)=.03 P(E)=.03

Answer 1

D.

Explanation:

Answer 2

By definition of conditional probability,


`\mathbb P(E\mid F)=(\mathbb P(E\cap F))/(\mathbb P(F))=(\mathbb P(F\mid E)\cdot\mathbb P(E))/(\mathbb P(F))`

We're told that
`\mathbb P(E\mid F)=\mathbb P(E)=0.03`, so


`0.03=(\mathbb P(F\mid E)\cdot0.03)/(\mathbb P(F))`

`1=(\mathbb P(F\mid E))/(\mathbb P(F))`

`\mathbb P(F)=\mathbb P(F\mid E)`

which means
`F` has the same chance of occurring regardless of whether or not
`E` had occurred. In other words,
`F` is independent of
`E`.