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

Answer 1

To determine if two events are independent using a two-way frequency table, you can look at the probabilities of each event occurring separately and then compare them to the joint probability of both events occurring together.

If the joint probability (the probability of both events happening) is equal to the product of the individual probabilities (the probability of one event happening multiplied by the probability of the other event happening), then the events are considered independent.

In a two-way frequency table, you can calculate the probabilities by dividing the frequency of each event by the total number of observations. If the calculated joint probability matches the product of the individual probabilities, then you can conclude that the events are independent.