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.
Similarities and Differences in a Random Sample of 375 Married Couples

Suppose that a married couple is selected at random.
(a) Use the data to estimate the probability that they will have exactly 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?

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Number of Similar Preferences All four Three Two One None Number of Married Couples 34 131 124 71 15