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

Question

Responses

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.

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

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 decide if two events are independent using a two-way frequency table, you should:

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

This means that if you calculate the probability of each event occurring individually and then multiply those probabilities together, the result should equal the probability of both events occurring together (the joint probability) for the events to be considered independent. This is the correct approach to determine independence in probability.