what statements are correct? check all that apply.\nthe conditional probability formula is…

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. In general, $P(D|N)=\frac{P(D\cap N)}{P(N)}$ and $P(N|D)=\frac{P(N\cap D)}{P(D)}$, and they are not equal unless $P(N) = P(D)$, 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 and independent events. For independent events, $P(X|Y)=P(X)$ when $X$ and $Y$ are independent, but it is still a conditional - probability calculation, so the fourth statement is incorrect.
  5. Conditional probabilities can be calculated using a Venn diagram by considering the overlapping regions and the size of the conditioning event's region, so the fifth statement is correct.

Answer:

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.