Question

If A and B are independent events, which equation must be true?
Options are in the picture

Answer 1

By definition of conditional probability,


`\mathbb P(X|Y)=(\mathbb P(X\cap Y))/(\mathbb P(Y))`

If
`X` and
`Y` are independent, then
`\mathbb P(X\cap Y)=\mathbb P(X)*\mathbb P(Y)`, which reduces the above probability to


`\mathbb P(X|Y)=(\mathbb P(X\cap Y))/(\mathbb P(Y))=(\mathbb P(X)*\mathbb P(Y))/(\mathbb P(Y))=\mathbb P(X)`

This means the answer is the second choice.