Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

What statements are correct? Check all that apply.

A. The conditional probability formula is [tex]$P(X \mid Y)=\frac{P(X \cap Y)}{P(Y)}$[/tex].
B. The conditional probabilities [tex]$P(D \mid N)$[/tex] and [tex][tex]$P(N \mid D)$[/tex][/tex] are equal for any events [tex]$D$[/tex] and [tex]$N$[/tex].
C. The notation [tex]$P(R \mid S)$[/tex] indicates the probability of event [tex][tex]$R$[/tex][/tex], given that event [tex]$S$[/tex] has already occurred.
D. Conditional probability applies only to independent events.
E. Conditional probabilities can be calculated using a Venn diagram.

Sagot :

GinnyAnswer
Sure, let's look at the provided statements about conditional probability and determine which ones are correct:

1. The conditional probability formula is [tex]$P(X \mid Y)=\frac{P(X \cap \cap}{P(\cap)}$[/tex]:

This statement appears to have a formatting issue that makes it hard to interpret correctly. If the intended formula is [tex]$P(X \mid Y) = \frac{P(X \cap Y)}{P(Y)}$[/tex], then it's correct. However, given the provided notation issue in the statement, it's better to mark this as incorrect.

2. The conditional probabilities [tex]$P(D \mid N)$[/tex] and [tex]$P(N \mid D)$[/tex] are equal for any events [tex]$D$[/tex] and [tex]$N$[/tex]:

This statement is incorrect. Conditional probabilities [tex]$P(D \mid N)$[/tex] and [tex]$P(N \mid D)$[/tex] are generally not equal. For example, if [tex]$D$[/tex] and [tex]$N$[/tex] are not independent events, then [tex]$P(D \mid N)$[/tex] can be very different from [tex]$P(N \mid D)$[/tex].

3. The notation [tex]$P(R \mid S)$[/tex] indicates the probability of event [tex]$R$[/tex], given that event [tex]$S$[/tex] has already occurred:

This statement is correct. The notation [tex]$P(R \mid S)$[/tex] correctly describes the conditional probability of [tex]$R$[/tex] given that [tex]$S$[/tex] has occurred.

4. Conditional probability applies only to independent events:

This statement is incorrect. Conditional probability is actually more relevant when dealing with dependent events. If two events are independent, then [tex]$P(R \mid S) = P(R)$[/tex], which trivializes the concept of conditional probability. Conditional probability helps describe the relationship between dependent events.

5. Conditional probabilities can be calculated using a Venn diagram:

This statement is correct. Venn diagrams can be used as a visual tool to help understand and calculate conditional probabilities by illustrating the overlap between events.

Therefore, the correct statements are:

- The notation [tex]$P(R \mid S)$[/tex] indicates the probability of event [tex]$R$[/tex], given that event [tex]$S$[/tex] has already occurred.
- Conditional probabilities can be calculated using a Venn diagram.

These correspond to statements 3 and 5.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.