How do I interpret P(A,B|C)

Question

I understand the joint and conditional probability, also the term P(A|B,C) . However, I don't really understand the term of P(A,B|C). Is that the event that when (A) happens and (B given C) happens?

Also when we get to the calculation, are we going to multiply those 2 terms P(A|C) and P(B|C) together to get the final result?

Thank you

Answer 1

This is $P(D\mid C)$ for $D=A\cap B$.