Understanding Basic Statistics 6th Edition by Charles Henry Brase,Corrinne Pellillo Brase

Exercise 79

Myers-Brigs: Personality Types Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates The following data give an indication (Source: I.B. Myers and M. H. McCaulley, A Guide to the Development and Use if the Myers-Briggs Type Indicators ).
Similarities and Differences in a Random Sample of 375 Married Couple

Suppose that a married couple is selected at random.
(a) Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common.
(b) Do the probabilities add up to 1 Why should they What is the sample space in this problem