In a relative frequency contingency tables, joint probabilities are located inside the margins.For each row of joint probabilities, in the right margin and same row, sum the joint probabilities. These are the row marginal probabilities. They are called marginal probabilities because they are located in a margin of the table. For each column, in the bottom margin and same column, sum the joint probabilities down the column. If the table has all the possible joint events, the sum of all column marginal probabilities equalsthe sum of all row marginal probabilities equals 1.

• Check thatthe sum of all column marginal probabilities equalsthe sum of all row marginal probabilities equals 1

Consider the following table of probabilities for events Cats, Dogs, Fish, which occur jointly with events hungryand not hungry:

The probability of joint event hungry Cats can be read directly from the table in B2 as 0.13.

For the marginal probability of event Cats, in B4 type = 0.13 + 0.05.

For the marginal probability of event hungry, in E2type = 0.13 + 0.17 + 0.15.

Suppose we have different probabilities:

P(Yes and Republican) is a ______ probability.