In a relative frequency continency 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 two 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 Colum, sum the joint probabilities down the column.If the table has all the possible joint events, the sum of all columns marginal probabilities equals the sum of all rows marginal probabilities equals 1.

Check the sum of all columns marginal probabilities equals the sum of all rows marginal probabilities equals 1

Consider the following table pf probabilities for events Cats, Dogs, Fish, which occurs jointly with events hungry and not hungry:

A B C D

1catsdogsfish

2 hungry0.130.170.15

3 not hungry0.050.250.25

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

For marginal probability of events Cats, in B4 type =0.13+0.15

For the mrginal probability of event hungry, in E2 type+0.13+0.17=0.15

Suppose we have different probabilities:

In favor democratsrepublicanrow total

Yes0.150.200.35

No0.250.400.65

Colum

Total0.400.601.0

P(Yes and Republican) is a _________probability

Answer:

a)Conditional

b)Marinal

c)Joint