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

Question

A. Two events are automatically independent because they have different values.
B. Show that the product of the two individual probabilities is equal to the combined probability of both from the two-way frequency table.
C. Show that the quotients of the two individual probabilities are equal to each other.
D. Two events have to have the same probability to be independent.

Answer 1

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

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

In more detail, two events A and B are independent if the probability of both A and B occurring together (denoted as P(A and B)) is equal to the product of the probabilities of each event occurring individually (P(A) * P(B)).

In the context of a two-way frequency table, you can find the probabilities by calculating:

1. The probability of event A (P(A)): Number of occurrences of A divided by the total number of observations.
2. The probability of event B (P(B)): Number of occurrences of B divided by the total number of observations.
3. The probability of both events occurring together (P(A and B)): The frequency count for the combination of A and B divided by the total number of observations.

You then check if P(A and B) = P(A) * P(B). If this equation holds true, the events are independent; otherwise, they are dependent.