How do you decide if two events are independent using a two-way frequency table?(1 point)

Question

Responses

Two events are automatically independent because they have different values.
Two events are automatically independent because they have different values.

Show that the quotients of the two individual probabilities are equal to each other.
Show that the quotients of the two individual probabilities are equal to each other.

Two events have to have the same probability to be independent.
Two events have to have the same probability to be independent.

Show that the product of the two individual probabilities is equal to the combined probability of both from the two-way frequency table.
Show that the product of the two individual probabilities is equal to the combined probability of both from the two-way frequency table.

Answer 1

To determine if two events are independent using a two-way frequency table, the correct approach is:

Show that the product of the two individual probabilities is equal to the combined probability of both from the two-way frequency table.

In mathematical terms, if \( P(A) \) and \( P(B) \) are the probabilities of events A and B, and \( P(A \text{ and } B) \) is the probability of both A and B occurring, then the events A and B are independent if:

\[ P(A \text{ and } B) = P(A) \times P(B) \]

If this equation holds true, then the two events are independent.