what statements are correct? check all that apply.\nthe conditional probability formula is $p(x |…

what statements are correct? check all that apply.\nthe conditional probability formula is $p(x | y)=\frac{p(xcap y)}{p(y)}$.\nthe conditional probabilities $p(d | n)$ and $p(n | d)$ are equal for any events d and n.\nthe notation $p(r | s)$ indicates the probability of event r, given that event s has already occurred.\nconditional probability applies only to independent events.\nconditional probabilities can be calculated using a venn diagram.

what statements are correct? check all that apply.\nthe conditional probability formula is $p(x | y)=\frac{p(xcap y)}{p(y)}$.\nthe conditional probabilities $p(d | n)$ and $p(n | d)$ are equal for any events d and n.\nthe notation $p(r | s)$ indicates the probability of event r, given that event s has already occurred.\nconditional probability applies only to independent events.\nconditional probabilities can be calculated using a venn diagram.

Answer

Brief Explanations:

  1. The conditional - probability formula is $P(X|Y)=\frac{P(X\cap Y)}{P(Y)}$, so the first statement is correct.
  2. $P(D|N)=\frac{P(D\cap N)}{P(N)}$ and $P(N|D)=\frac{P(N\cap D)}{P(D)}$, and they are not equal in general, so the second statement is incorrect.
  3. The notation $P(R|S)$ indeed represents the probability of event $R$ given that event $S$ has occurred, so the third statement is correct.
  4. Conditional - probability applies to dependent events, not just independent events, so the fourth statement is incorrect.
  5. Conditional probabilities can be calculated using a Venn diagram by considering the overlapping and non - overlapping regions of the events, so the fifth statement is correct.

Answer:

The correct statements are: The conditional probability formula is $P(X|Y)=\frac{P(X\cap Y)}{P(Y)}$. The notation $P(R|S)$ indicates the probability of event $R$, given that event $S$ has already occurred. Conditional probabilities can be calculated using a Venn diagram.