Conditional Probability and Bayes' Formula Questions

[sampahmel]

Dear all,

Please clarify the following:

1.) The difference of conditional probability and Bayes' formula.

2.) Is Bayes' formula a "all weather condition" formula for all conditional probabilities problem?


Thank you,

S

 

[sampahmel]

Can anyone please answer to the above question?

 

[Focus]

1) Conditional probability is $$\mathbb{P}(A|B):=\frac{\mathbb{P}(A \cap B)}{\mathbb{P}(B)}$$.

Bayes Theorem is used to swap the condition around,
$$\mathbb{P}(A|B):=\frac{\mathbb{P}(B|A) \mathbb{P}(A)}{\mathbb{P}(B)}$$

2) You can use Bayes formula for any conditional probabilities such that $$\mathbb{P}(B)>0$$