So which notation do I use? Which of the following is the appropriate notation when calculating conditional probabilities?

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So which notation do I use? Which of the following is the appropriate notation when calculating conditional probabilities?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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And is 'union' interchangeable with 'and'?
no, since "union" is interchangeable with "or"

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So that would be the upside union sign then?
"intersection" is interchangeable, with "and", and its symbol is the upside union symbol
Okay, so then can I eliminate option B as a possible answer?
yes!
Sweet! And also A as it has a union sign or no?
in order to compute the conditional probability, we can eliminate the first two options
  • phi
To answer this one, you need to know the definition of conditional probability some of the choices are correct, but not related to conditional probability
Okay, thanks.
Oh, the answer is C Because it needs to be over P(A) not P(B) which in this case is C and D, respectively.
Correct?
I think that C is not the answer since the conditional probability involves the probabilities of 2 correlated or uncorrelated distinct events
Oh, you're right. It would be over P(C) if C was the second term. But it is P(C | D) not P(C | C). I get it, thank you @Michele_Laino
  • phi
P(C | D ) means probability of C given that D occurs it is the intersection of C and D divided by the chance of D occuring
:)
*not P(D | C)
the definition of conditional probability is: \[P\left( {C \cap D} \right) = P\left( D \right)P\left( {C|D} \right)\] namely the probability for intersection, is equal to the probability of the first event D times the probability of the other event C, when D is occurred

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