Question

So which notation do I use?


Which of the following is the appropriate notation when calculating conditional probabilities?

Answer 1

And is 'union' interchangeable with 'and'?

Answer 2

no, since "union" is interchangeable with "or"

Answer 3

So that would be the upside union sign then?

Answer 4

"intersection" is interchangeable, with "and", and its symbol is the upside union symbol

Answer 5

Okay, so then can I eliminate option B as a possible answer?

Answer 6

yes!

Answer 7

Sweet! And also A as it has a union sign or no?

Answer 8

in order to compute the conditional probability, we can eliminate the first two options

Answer 9

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

Answer 10

Okay, thanks.

Answer 11

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.

Answer 12

Correct?

Answer 13

I think that C is not the answer since the conditional probability involves the probabilities of 2 correlated or uncorrelated distinct events

Answer 14

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

Answer 15

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

Answer 16

:)

Answer 17

*not P(D | C)

Answer 18

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