# Probability of $A$ given $A$ intersection $B$ [closed]

Two dice are rolled, and $A$ and $B$ stand for: $A=$ first of the numbers is an odd number, $B=$ the sum of the numbers is $4$.

How do I write down this probability?

## closed as unclear what you're asking by Did, Jose Arnaldo Bebita-Dris, Shailesh, ccorn, rtybaseSep 2 '18 at 16:33

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• Given $A$ and $B$ have both happened, what is the probability that $A$ has happened? – GoodDeeds Sep 2 '18 at 11:14
• What do you mean by probability of $A$ given $A \cap B$ ? Really $\mathbb{P}(A | A \cap B)$ ? – LucaMac Sep 2 '18 at 11:15
• Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments. – José Carlos Santos Sep 2 '18 at 11:17
• P(A|A ∩B) <--- that's how it looks like, it's a homework and I don't know how to write and calculate that correctly. – user589214 Sep 2 '18 at 11:20

## 1 Answer

$P(A|A \cap B) = \frac{P(A \cap A \cap B)}{P(A \cap B)} = \frac{P(A \cap B)}{P(A \cap B)} = 1$

• Quite the same I got earlier myself, I just wasn't certain of it. Thank you :) – user589214 Sep 2 '18 at 11:46