MathProbabilityEvents and probabilities

Conditional probability

Equal or not?

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Which of the following statements is correct for an arbitrary $A$ ?

$\mathbb{P}(A) < \mathbb{P}(A | A) < \mathbb{P}(A \cap A)$
$\mathbb{P}(A) > \mathbb{P}(A | A) > \mathbb{P}(A \cap A)$
$\mathbb{P} (A) = \mathbb{P}(A \cap A)$ and $\mathbb{P}(A) \leq \mathbb{P}(A | A)$
$\mathbb{P}(A) =\mathbb{P}(A \cap A)$ and $\mathbb{P}(A | A) = \mathbb{P}(A)$

Select one option from the list

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